Question

What is Cube root of 125 x Superscript 12?

A. 5x2
B. 5x4
C. 25x2
D. 25x4

Answer 1

Answer: B) 5x^4

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Work Shown:

125 = 5*5*5 = (5)^3

x^12 = (x^4)*(x^4)*(x^4) = (x^4)^3

125x^12 = (5x^4)^3

`\large \sqrt[3]{125x^(12)} = \left(125x^(12)\right)^(1/3)`

`\large \sqrt[3]{125x^(12)} = \left((5x^4)^3\right)^(1/3)`

`\large \sqrt[3]{125x^(12)} = (5x^4)^(3*(1/3))`

`\large \sqrt[3]{125x^(12)} = (5x^4)^(1)`

`\large \sqrt[3]{125x^(12)} = \textbf{5x}^{\textbf{4}}`

Answer 2

Explanation:

`125=5*5*5=5^(3)\\\\\ \sqrt[3]{125x^(12)}=\sqrt[3]{125*x^(4*3)}\\\\=\sqrt[3]{5^(3)*(x^(4))^(3)}=5*x^(4)=5x^(4)`