Question

NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.

Answer 1

Answer: Choice B)   72a^3

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Explanation:

We have something of the form [M*N]^2 where M = 3 and N = (2a)^(3/2)

Squaring the M leads to M^2 = 3^2 = 9

Squaring the N leads to N^2 = (2a)^3 = 8a^3

Notice how the fractional exponent goes away. The denominator '2' cancels with the '2' from the squaring operation

In other words, the rule is $\left(x^{1/2}\right)^2 = x$ where x is nonnegative.

A more general form of the rule is $\left(x^{p/2}\right)^2 = x^p$

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After squaring M and N, we then get to

[MN]^2 = M^2*N^2 =  9*8a^3 = 72a^3

So that shows why choice B is the answer.