Question

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

Simplify: [3(2a)^3/2]^2

A: 34^4√2a^9

B: 72a^3

C: 216a^3

D: 24a^3​

Answer 1

Answer: Choice B) 72a^3

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Step-by-step 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.