Question

Simplify: 4^ sqrt 400/ 4^ sqrt 5
SHOW WORK

Answer 1

Given  

The equation is in the form

$=\frac{4^{\sqrt{400}}}{4^{\sqrt{5}}}$

Simplify the above equation

To proof

As given in the question the equation is written in the form

$=\frac{4^{\sqrt{400}}}{4^{\sqrt{5}}}$

By using the exponent property

when you divide powers with the same base you just have to subtract the exponents. i.e

$\frac{y^{a}}{y^{b}} = y^{a-b}$

y is not equal to zero.

Now apply this property to the above equation

$=4^{\sqrt{400}- \sqrt{5}}$

As

$\sqrt{400} = 20$

now put this in the above equation

we get

$=4^{20- \sqrt{5}}$

Hence proved