Question

What is the following product

Answer 1

Answer:

Step-by-step explanation:

Here we are multiplying one fifth root of a quantity by another 5th root of another quantity.

Changing from radical to fractional exponent form yields

(4x^2)^(1/5)*(4x^2)^(1/5).  Actually, this is identical to the square of (4x^2)^(1/5);

(4x^2)^(2/5).  This is equivalent to  4^(2/5)*(x^2)^(2/5), or

16^(1/5)*(x^4)^(1/5).  This is the 5th root of 16x^4, which is the 2nd answer choice.

Answer 2

The product of the indices is $\sqrt[5]{16x^2}$. Option A is correct

Given the indices expressed as:

$\sqrt[5]{4x^2} \cdot \sqrt[5]{4x^2}$

This can be expressed as"

$(4x^2)^{\frac{1}{5} } \times (4x^2)^{\frac{1}{5} }$

According to the law of indices;

$a^m \times a^n = a^{m+n$

Applying this rule will give;

$(4x^2)^{\frac{1}{5} } \times (4x^2)^{\frac{1}{5} } = (4x^2)^{1/5+1/5}\\=(4x^2)^{2/5}\\= \sqrt[5]{(4x)^2} \\=\sqrt[5]{16x^2}$

Hence the product of the indices is $\sqrt[5]{16x^2}$

Learn more on indices here: https://brainly.com/question/8952483