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Question 237219: ahhmmm... im not really good at this... I'm just confused in law of exponents..
for example: 12a to the 3rd power.. over 4b to the 2nd power.... or,, (16a)to the 2nd power or (16a)cube... its very difficult,, pls. give me some tips or tell me whats the rules in solving those problems.. I hope you really answer my question... Im only 13 yrs old,, and im not a fast learner..
thank you Patty.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the rules of exponents are
b^x * b^y = b^(x+y) example 2^2 * 2^3 = 2^(2+3) = 2^5 = 32.
this is equivalent to (2*2)*(2*2*2) = 2*2*2*2*2 = 32.
b^x / b^y = b^(x-y) example 2^5 / 2^3 = 2^(5-3) = 2^2 = 4
this is equivalent to 2*2*2*2*2/2*2*2 = 2*2 = 4
(b^x)^y = b^(x*y) example (2^3)^3 = 2^(3*3) = 2^9 = 512
this is equivalent to (2*2*2)^3 = (2*2*2)*(2*2*2)*2*2*2) = 2*2*2*2*2*2*2*2*2 = 512
b^(-x) = 1/b^x example 2^(-2) = 1/2^2 = 1/4
this is equivalent to 1/(2*2) = 1/4
if you put this in your calculator and ask the calculator to solve for 2^(-2) the calculator will tell you the answer is .25. if you put 1/(2^2) in the calculator it will tell you the same thing.
b^(1/x) = root(x,b) example 512^(1/9) = root(9,512) = 2
root(9,512) means the 9th root of 512.
root(2,4) would be the square root of 4
root(3,27) would be the cube root of 27, etc.
all of the above rules imply the same base.
2^4 * 2^2 = 2^(4+2) = 2^6 = 64 because they both have the same base.
2^4 * 3^2 do NOT have the same base so you can't combine them. this is simply 2^4 * 3^2 and cannot be reduced any further.
always check your work with the calculator.
if the problem is 2^5 / 2^2, you can put that in your calculator and solve directly to get an answer of 8
you can slso reduce it by using the rules above to make 2^5 / 2^2 = 2^(5-2) = 2^3 = 2*2*2 = 8.
if you get the same answer by doing it both ways, then you did it right.
you should try the following websites to help you understand exponents better if you're having a hard time.
exponents from purple math
exponents from west texas a&m university
your examples were:
12a to the 3rd power.. over 4b to the 2nd power.... or,, (16a)to the 2nd power or (16a)cube... its very difficult,,
12a to the third power is equal to 12*a^3 which means 12 * a*a*a
(12a) to the third power is equal to (12a)^3 which means (12a)*(12a)*(12a)
those parentheses make a difference.
12a^3/4b^2 would not be able to be reduced any further because they have dirrent bases. you could divide 4 into 12 to get 3a^3/b^2 but that's as far as you could go.
if they had common bases, then your equation would look like 12a^3/4a^2 which could be reduced as follos:
12a^3/4a^2 = 3a^3/4a^2 once we divide by 4.
it then equals 3*a(3-2) because a^3/a^2 = a^(3-2)
think of a^3 = a*a*a and a^2 as a*a and you get a*a*a/a*a.
2 of the a's cancel out and you are left with 1 a on top.
this is equivalent to a^(3-2).
16a^3 is the same as 16a^3 is the same as 16*a*a*a
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