Question

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

Answer 1

Given

The equation is in the form

`=(4^(√(400)))/(4^(√(5)))`

Simplify the above equation

To proof

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

`=(4^(√(400)))/(4^(√(5)))`

By using the exponent property

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

`(y^(a))/(y^(b)) = y^(a-b)`

y is not equal to zero.

Now apply this property to the above equation

`=4^(√(400)- √(5))`

As

`√(400) = 20`

now put this in the above equation

we get

`=4^(20- √(5))`

Hence proved