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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 [tex]\left(x^{1/2}\right)^2 = x[/tex] where x is nonnegative.
A more general form of the rule is [tex]\left(x^{p/2}\right)^2 = x^p[/tex]
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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.
