SOLUTION: Simplify the expression. Do not use negative exponents in the answer. (1/4x^7)^3 (x^3)^6 I am really confused on this problem. anyone suggestion would be great on how t

Algebra ->  Volume -> SOLUTION: Simplify the expression. Do not use negative exponents in the answer. (1/4x^7)^3 (x^3)^6 I am really confused on this problem. anyone suggestion would be great on how t      Log On


   

Question 319203:
Simplify the expression. Do not use negative exponents in the answer.

(1/4x^7)^3 (x^3)^6
I am really confused on this problem. anyone suggestion would be great on how to do this problem?
Found 3 solutions by jim_thompson5910, mananth, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F%284x%5E7%29%29%5E3+%28x%5E3%29%5E6+ Start with the given expression.


%28%281%5E3%29%2F%284x%5E7%29%5E3%29%28x%5E3%29%5E6+ Distribute the exponent.


%28%281%5E3%29%2F%284%5E3%28x%5E7%29%5E3%29%29%28x%5E3%29%5E6+ Distribute the exponent again.


%28%281%5E3%29%2F%2864%28x%5E7%29%5E3%29%29%28x%5E3%29%5E6+ Raise 4 to the third power to get 64.


%28%281%5E3%29%2F%2864x%5E%287%2A3%29%29%29%28x%5E%283%2A6%29%29+ Multiply the exponents.


%28%281%5E3%29%2F%2864x%5E%2821%29%29%29%28x%5E%2818%29%29+ Multiply.


%281%2F%2864x%5E%2821%29%29%29%28x%5E%2818%29%29+ Raise 1 to the third power to get 1.


x%5E%2818%29%2F64x%5E%2821%29+ Combine the fractions.


x%5E%2818-21%29%2F64+ Subtract the exponents to divide.


x%5E%28-3%29%2F64+ Subtract.


1%2F%2864x%5E3%29+ Flip the base with the negative exponent.


So %281%2F%284x%5E7%29%29%5E3%28x%5E3%29%5E6=1%2F%2864x%5E3%29+

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(1/4x^7)^3 (x^3)^6
1/64 x^21 * x^18
1/64 * x^39

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(1/4x^7)^3 (x^3)^6
----------------------------
Assuming the 4x^7 is in the denominator of the 1st fraction I get:
(1/(64x^21))*(x^18)
----
= (1/64)(x^18/x^21)
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= (1/64)(1/x^3)
---
= 1/(64x^3)
====================
Cheers,
Stan H.