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

A. 6

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^{(6)/(3)}\cdot5^{(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