Question

rewrite with a sinle exponent (9^7)^3

Answer 1

=9^(7*3)=9^21

Answer 2

In general
\[(a^x)^y = a^{xy}.\]

Hence the result people are giving you above.

Answer 3

??

Answer 4

For example
\[(2^5)^3 = 2^{5 \ times \ 3} = 2^{15}\]
In the example I just did, a = a, x = 5 and y = 3
Beginning to make sense?

Answer 5

You can see this explicitly if you write it out.

What does (2^5)^3 mean? It means first of all 2^5 multiplied out three times

\[(2^5)^3 = 2^5 . 2^5 . 2^5\]
Now this is equal to
\[2^{5 + 5 + 5} = 2^{5 \ \times \ 3} = 2^{15}\]