Tutors Answer Your Questions about Exponents (FREE)
Question 570176: When rewriting an exponential expression with a negative exponent and a positive base to an expression containing only a positive exponent, does the sign of the base change?
Answer by stanbon(48516)  (Show Source):
Question 570073: How do I work this problem: 64-6[15+2(-3+8)]? I have tried five times using PEMDAS without success in getting to the answer of -86. Thank you.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(21667) (Show Source):
You can put this solution on YOUR website!64-6[15+2(-3+8)] ... Start with the given expression
64-6[15+2(5)] ... Add -3 to 8 to get 5
64-6[15+10] ... Multiply 2 and 5 to get 10
64-6[25] ... Add 15 to 10 to get 25
64-150 ... Multiply -6 and 25 to get -150
-86 ... Subtract 150 from 64 to get -86
So 64-6[15+2(-3+8)] = -86
Answer by stanbon(48516) (Show Source):
Question 568422: Let f(x) = 3x. Find f( 3) and f(1/3).
Answer by jim_thompson5910(21667) (Show Source):
Question 568828: what is the answer to 2z raised to the -8 power
Answer by jim_thompson5910(21667) (Show Source):
Question 568807: (2x2)-4 answer should contain only positive exponents
Answer by Alan3354(21555)  (Show Source):
Question 568734: Hi I'm an 8th grade Algebra I student and i don't understand this problem. Please show your work thoroughly. Thanks!!!!
2^n * 2^n+2*2
(The n+2 is all raised, not just the n.)
Thank you once more!!!!!!!!!!!!!!!!!!!!!!
Answer by stanbon(48516) (Show Source):
You can put this solution on YOUR website!2^n * 2^(n+2)*2
-----
Since the bases are the same you should
add the exponents when you multiply.
-----
= 2^[n + n+2 + 1]
-----
= 2^[2n+3]
==============
Cheers,
Stan H.
==============
Question 568742: Hi I'm in Algebra I 8th grade and I don't understand how to do this problem.
Please show work and explain step by step. Thanks!!!!
5^x+1 * 5^1-x
(The x+1 and 1-x are both raised to both fives)
THANK YOU!!!!
Answer by solver91311(12118)  (Show Source):
Question 568718: Hi I'm in Algebra I 8th grade and I don't understand how to do this problem. Please show work and explain step by step. Thanks!!!!
3^x * 3^2-x * 3^2
(The 2-x is raised, not just the 2; it's not 3^2= 9 - x, the 2 and -x are both raised.)
THANK YOU!!!!
Answer by solver91311(12118) (Show Source):
Question 568385: what are the steps way to solve this equations: 48xy/48x
Answer by jim_thompson5910(21667) (Show Source):
You can put this solution on YOUR website!Divide 48 into 48 to get 1
Then divide xy into x to get y (since x/x = 1)
So  for all values of x and y (where x is not zero)
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If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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Question 567073: im knew to algebra, and i don't know how to attack it, do u think u can help me out.
1. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number?
A. ZY - V
B. Z/V - 3 - Y
C. Z/3 - V - Y
D. 3V- Z - Y
E. V- Z - Y
Answer by richard1234(4789)  (Show Source):
You can put this solution on YOUR website!Let X be the remaining number. Since the average of X,Y,Z is V, we have
Subtract Y+Z from both sides to isolate X.
This is the same as answer choice D.
Question 566900: what do you do to find 4 to the 3rd power?
PLEASE HELP!
Answer by Alan3354(21555) (Show Source):
Question 566409: My question is what would this be simplified . I am using ^ as a power.
(4xy^2)^4
----------
(3xy^2)^4 They are being divided and also the power to 4 goes for
both.
Thanks so much!
Answer by mananth(10541)  (Show Source):
Question 565840: complete the prime factorization of 243 using exponents when possible
Answer by ad_alta(170)  (Show Source):
Question 565424: Solve for x:
Answer by htmentor(580)  (Show Source):
You can put this solution on YOUR website!Solve for x:
===================================
We can factor the expression as follows:
From here, we can read off the answer x = 1/2, or solve using logarithms:
Dividing through be log(7) gives x = 1/2
Question 565341: Please tell me if I'm working this out right..
First I did what was in []... (-2*-2)-2|-2= (4)-2|-2|= 0
Is that right so far?
Then I took the numerator.. -2*-2= 4 So, now it's 4/ 2-2*0= 4/0 or 4.
Am I even close? It's been a very long time since I learned this stuff. I only hope you're seeing the equation as I am. Thanks for your help.
Answer by Tias_411(14)  (Show Source):
You can put this solution on YOUR website!
first... your [] works out like, (-2)^2 - 2*|-2|
4 - 2*(2)
4-4= 0 so yes, that part is right. But you also have 2-2 multiplied by whatever is in your [].
2-2*(0)
2-0
2 this means your denominator is 2.
then work out the numerator... (-2)^2 = 4
now that you have your numerator and denominator your answer is 4/2 and in simplest form that's expressed as 2/1 or just 2.
**use PEMDAS when doing equations.. multiply or divide BEFORE adding or subtracting. so you multiply 2 by [] then subtract that from 2.
Question 564981: I am trying to solve this Problem. Please help. thank you.
The flow of water F in cubic feet per second over a wier, a small overflow dam, can be represented by F=1.26H2/3, where H is the height of the water in meters above the crest of the wier. Find the height of the water if the flow of the water is 10.08 cubic feet per second.
Answer by ankor@dixie-net.com(12684)  (Show Source):
You can put this solution on YOUR website!The flow of water F in cubic feet per second over a wier, a small overflow dam, can be represented by F=1.26H2/3, where H is the height of the water in meters above the crest of the wier.
Find the height of the water if the flow of the water is 10.08 cubic feet per
second
:
1.26H*  = 10.8
multiply both sides by 3
1.26H(2) = 10.8*3
2.52H = 32.4
H = 
H = 12.857 ~ 13 meters
Question 564034: i need help explaining in details this promblem -3(5-6)-4(2-3)
Answer by stanbon(48516) (Show Source):
You can put this solution on YOUR website!-3(5-6)-4(2-3)
-------------
Evaluate each parenthesis:
= -3(-1)-4(-1)
----
Multiply each product to get:
= 3 + 4
---
= 7
=============
Cheers,
Stan H.
Question 563933: how to solve 2x^3 + 2=0
Answer by TutorDelphia(189)  (Show Source):
You can put this solution on YOUR website!This problem looks tricky but can actually be solved in just a few steps
2x^3 + 2=0
subtract 2 from both sides
2x^3=-2
divide both sides by 2
x^3=-1
Take the cube root of both sides, which will give you
x=-1
since -1*-1*-1=-1
Question 563497: What is 4/x^3 without using the fraction bar?
Answer by nerdybill(5404)  (Show Source):
Question 562819: (16-3)*4
Answer by issacodegard(60)  (Show Source):
Question 562767: write the expression without using a fraction bar-
9a2/b6
Answer by issacodegard(60) (Show Source):
Question 562391: How to simplify:
(4x3)2
Answer by Edwin McCravy(6932)  (Show Source):
You can put this solution on YOUR website!
How to simplify
(4x3)2
Give the 4 a 1 exponent:
(41x3)2
To remove the parentheses, multiply each exponent inside
the parentheses by the exponent outside the parentheses
41*2x3*2
42x6
16x6
Edwin
Question 562143: Please help me solve this problem. 
Answer by mananth(10541) (Show Source):
Question 561603: i don't get this stuff on exponets! please help! the question is:
n^-6*n^-9
Answer by Edwin McCravy(6932) (Show Source):
Question 561035: (-4.2)^2
I get 17.64, but the book says the correct answer is 16.81
Found 2 solutions by richard1234, jim_thompson5910:
Answer by richard1234(4789) (Show Source):
Answer by jim_thompson5910(21667) (Show Source):
You can put this solution on YOUR website!You are correct. I can tell right off the bat that you are correct (or at least more correct) since the units digit is correct. The answer choice's units digit is way off.
Question 560792:
Answer by jim_thompson5910(21667) (Show Source):
Question 559338: Could you help me solve the equation of 
Answer by josmiceli(6778)  (Show Source):
You can put this solution on YOUR website!
You can solve by completing the square.
Take 1/2 of the coefficient of  ,
square it, and add it to both sides
Take the square root of both sides
and also, taking the negative square root,
------------------
I will attempt to check the 1st solution
OK
You can check the other solution,
Question 558797: How do u do this (2t5)3?
Answer by rapaljer(4551)  (Show Source):
You can put this solution on YOUR website!
For additional examples and explanation on the Laws of Exponents, please see my website. To go to my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. At the very bottom of this page, there is a link that will take you to my Homepage.
Once you are on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 2," Section 2.12 for a complete, non-traditional explanation that my own students, before I retired, found a lot easier to understand than the published textbooks of that day. You should really like my MATH IN LIVING COLOR pages, where the most difficult problems are solved IN COLOR.
Everything on the website is FREE. If you find something you really like, just print your own copy of it!!
If anyone needs to contact me, especially about the website, my Email address is rapaljer@seminolestate.edu. I'll be glad to help you find an explanation on my website to help you with your algebra topic!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 558348: Raise the quantity in the parentheses to the indicated exponent and simplify the resulting expression. Express answers with positive exponents.
(-36x^2y/180x^-3y^-5)^-2
(-16x^-2y^3/80x^-2y^3)^2
Answer by saifoo.khan(153)  (Show Source):
Question 558011: 1.)Solve the equation 2^(2x – 1) = 8^(x + 7).
2.)Solve the equation 3^x = 3^(3x + 1).
3.)Solve the equation (1/3)^x = 3^(x – 6).
I just can't figure these out. Thanks so much for helping!!!
Answer by KMST(578)  (Show Source):
You can put this solution on YOUR website!1.) 
Since  , substituting in the equation given, we get
 and applying the properties of exponents, that simplifies to
 , which simplifies further to
Since both sides are powers of the same base (2), the exponents must be equal, so we solve
 -->  --> 
Checking:  and 
2.) 
Since both sides are powers of the same base (3), the exponents must be equal, so we solve
 -->  -->  --> 
3.) 
 , so we can write the equation as
 and applying the properties of exponents, that simplifies to
Since both sides are powers of the same base (3), the exponents must be equal, so we solve
 -->  -->  -->  -->  --> 
Question 558068: what is n to the 4th power divided by n to the 8 power?
Answer by KMST(578) (Show Source):
Question 558066: Simplify the following product of complex numbers.
(8 + i) · (-4 – 3i)
Answer by solver91311(12118) (Show Source):
You can put this solution on YOUR website!
Just use the FOIL process like multiplying any other pair of binomials. Remember that 
John
My calculator said it, I believe it, that settles it
Question 558035: (3m^-3)^2/m^-4
Answer by stanbon(48516) (Show Source):
Question 557900: 16^-3/4
Answer by rfer(10417) (Show Source):
Question 557665: Im having problems wit this particular expression. Could someone help me out please
(16x^8y^12)1/2
(161/2)(x^8)1/2(y^12)1/2
(16)^-1 x^4 y^6
1/16 1/x^4 1/y^6
y^6/16x^4
Answer by KMST(578) (Show Source):
You can put this solution on YOUR website!Your question is confusing, so I assume you are confused. As a result I may end up answering the wrong question, or confusing you even worse.
Maybe your expression was
If so the answer is
=  = 
There was not much anyone could do with that expression.
There are a few "grammar" rules for reading and writing algebra. They are very few. The rest are logical conclusions, like the need to take off your shoes before taking off your socks. They are obvious if you are not in panic mode. Unfortunately math and algebra cause a lot of unnecessary panic.
The "grammar" rules for writing algebra say that  means that  and  would be calculated first, if you could do it.
However, there's nothing you can do with them, so they will carry unchanged to the end, like so much undigestible fiber.
You have three factors inside the parenthesis:  , and .
A fourth factor  is outside the parenthesis.
All four factors are multiplied together. Although multiplication is done two factors at a time, when all you are doing is multiplications, the order and the grouping do not matter. So when they write the calculation for the volume of a box as
 it really means  , but no one bother to write the parentheses.
The result can also be calculated as  or as  . You will use all your factors, but can choose how to do it. You grab any two factors, multiply them together, and then multiply the result times the other factor. You would not care which two dimensions of a box you multiply together first. The volume of the box is the same, anyway you calculate it.
In the case of your problem, the only two factors you can do anything with are and , so after you multiply those two together, you are done. You leave the rest of the multiplications indicated.
Question 556713: (5^3)^-8
They want the exponential notation to be positive and I have no clue how to do that.
Answer by Edwin McCravy(6932) (Show Source):
Question 556083: please help (-12 to the 2nd power all in parenthesis) I am stumped !!
Answer by jim_thompson5910(21667) (Show Source):
Question 555387: (-5^6)(2^3)
Answer by jim_thompson5910(21667) (Show Source):
Question 554600: What is the Least Common Multiple of  and 
Answer by ankor@dixie-net.com(12684) (Show Source):
Question 554605: What is the Least Common Multiple of  and 
Answer by ankor@dixie-net.com(12684) (Show Source):
Question 554748: 3 square root of 13+7 square root of 13
Answer by jim_thompson5910(21667) (Show Source):
Question 554745: Need help to simplify square root of 12. I think it is 4 but not sure.
Need help to simplify square root of 75. Not sure at all on this one.
Answer by jim_thompson5910(21667) (Show Source):
Question 554153: I need to evaluate or simplify this numerical expression
(16)to 3/4 of ? power
Answer by stanbon(48516) (Show Source):
You can put this solution on YOUR website!I need to evaluate or simplify this numerical expression
(16)to 3/4 of ? power
----
The 4 in the denominator means "take the 4th root"
You get:
= (2)^3
----
The 3 in the numerator means "cube":
= 8
==========
Cheers,
Stan H.
============
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