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

Answer:

Step-by-step explanation:

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