Question

What is the following product? RootIndex 5 StartRoot 4 x squared EndRoot times RootIndex 5 StartRoot 4 x squared EndRoot.

Answer 1

You can use the fact that whenever bases are same, the product of such quantities end up getting their exponents added.

The product result of given expression is $^5\sqrt{(2x)^4}$

When does the power add in multiplication?

Suppose you've got two values to multiply with each other and you have got both value's bases same, then the multiplication will end up with result being that base raised with sum of the exponents of both the initial values.

For example:

$a^b \times ^c =a^{b+c}$

How to find the product result for given expression?

You can convert the roots to powers. Then you can use the fact that the bases are same and thus the powers will add.

Remember that if you've got xth root, then the power would be 1/x.

For our case, it will go like this:

$^5\sqrt{4x^2} \times ^5\sqrt{4x^2} = \: ^5\sqrt{(2x)^2} \times ^5\sqrt{(2x)^2} = {((2x)^2)}^{\frac{1}{5}} \times {((2x)^2)}^{\frac{1}{5}} = (2x)^{\frac{2}{5}} \times (2x)^{\frac{2}{5}}\\\\ ^5\sqrt{4x^2} \times ^5\sqrt{4x^2} = (2x)^{\frac{2}{5} + \frac{2}{5}} = (2x)^{\frac{4}{5}} = \: ^5\sqrt{(2x)^4}$

Thus, the final product result will be written as $^5\sqrt{(2x)^4}$

Learn more about base and exponent here:

https://brainly.com/question/9047706