Let k be the result of squaring the base and tripling the exponent of a^b, a>b>1.?

Question

If k also equals the product of a^b and c^b, then c equals:

Answer 1

So k = (a^2)^(3b) = a^(2 * 3b) = a^(6b).
We also know k = a^b * c^b.
So a^(6b) = a^b * c^b.
So a^(5b) = c^b.
So (a^5)^b=c^b.
So c = a^5.

Answer 2

Let k be the result of squaring the base and tripling the exponent of a^b, a>b>1.?
If k also equals the product of a^b and c^b, then c equals

k = (a^2)^(3b)
= a^(6b)
k = a^b.c^b

So a^(6b) = a^b.c^b
c^b = a^(6b)/a^b
= a^(6b)*a^(-b)
= a^5b
= (a^5)^b

Thus c = a^5

Answer 3

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