What is [3(2a)^{3/2}]^2 ?

The solution to [3(2a)^{3/2}]^2 is 72a^3

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simplify [3(2a)^{3/2}]^2

simplify

[3 (2 a)^{\frac{3}{2}}]^{2}

72 a^{3}

Solution steps

(3 (2 a)^{\frac{3}{2}})^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 (2 a)^{\frac{3}{2}})^{2} = 3^{2} ((2 a)^{\frac{3}{2}})^{2}

= 3^{2} ((2 a)^{\frac{3}{2}})^{2}

3^{2} = 9

= 9 ((2 a)^{\frac{3}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

((2 a)^{\frac{3}{2}})^{2} = (2 a)^{\frac{3}{2} \cdot 2}

= 9 (2 a)^{\frac{3}{2} \cdot 2}

\frac{3}{2} \cdot 2 = 3

= 9 (2 a)^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 a)^{3} = 2^{3} a^{3}

= 9 \cdot 2^{3} a^{3}

2^{3} = 8

= 9 \cdot 8 a^{3}

Multiply the numbers:

9 \cdot 8 = 72

= 72 a^{3}

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