SOLUTION: Simplify. (a^3)^6

Question 114176: Simplify. (a^3)^6
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
For this problem, the power rule of exponents applies. That rule states that when you raise
a quantity that has an exponent to a power, you multiply the exponents and use this product
as the exponent of the base. For example:
.

.
Applying this rule to your problem you have:
.

.
and the answer you are looking for is
.
you can also look at it this way:
.
by definition. If you raise to the 6th power you multiply it
by itself 6 times. That is you have:
.

.
but then on the right side you can replace each by and when you
do that the equation becomes:
.

.
and when you count all the a's on the right side you get 18 of them, all multiplied
together. This means that:
.

.
which is the same answer that we got when we multiplied the exponent 3 times the exponent 6
to get the resulting exponent of 18.
.
Hope this helps you to see what is going on with this problem.
.

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