Question

Given n = 2^6 x 5^12 and the cube root of n = 2^a x 5^b, what is the sum of a +b

Answer 1

ANSWER:

A. 6

STEP-BY-STEP EXPLANATION:

We have the following expression;

$N=2^6\cdot5^{12}$

Now, to the value of N we apply the cube root and we are left with the following:

$\begin{gathered} \sqrt[3]{N}=\sqrt[3]{2^6\cdot5^{12}}=2^{\frac{6}{3}}\cdot5^{\frac{12}{3}}=2^2\cdot5^4 \\ \\ \text{ Therefore, a = 2 and b = 4} \\ \\ \text{ so, we replacing} \\ \\ a+b=2+4=6 \end{gathered}$

This means that the correct answer is A. 6