Question

Simplify the given expression. Show all steps. Submit your handwritten work or use the equation editor to receive credit.

Answer 1

1/x² = x^(-2)

Explanation:

((x¹⁰)^(1/5))/sqrt(x⁸)

4 things are important to remember here :

• when we put an exponent on an exponent, we multiply both exponents.
• when we multiply terms with the same base, we add the exponents, and when we divide, we subtract the exponents.
• a negative sign in the exponent means 1/...
• and a fraction as exponent is defined as

`{x}^(a / b) = \sqrt[b]{ {x}^(a) }`

so, for example, a square root is the same as 1/2 as exponent.

now we can simplify.

let's start with the numerator :

(x¹⁰)^(1/5) = x^(10×1/5) = x²

then the denominator :

sqrt(x⁸) = x^(8×1/2) = x⁴

the whole fraction looks like

x²/x⁴

remember about the subtraction of exponents when dividing :

x²/x⁴ = x^(2-4) = x^-2 = 1/x²

FYI

when you remember, what an exponent actually is : the number how often the base had to be multiplied by itself, ...

x×x / x×x×x×x

the top 2 x can be reduced to 1 by division by 2 of the bottom x.

what is left is 1/x²

Answer 2

`(1)/(x^2)`

Explanation:

first, simplify
`(x^(10))^(1)/(5)`
`(10)/(1) =(1)/(5)` , 5 and 10 cancel each other, so
`(2)/(1)` or 2.
`x^2`

secondly,
`√(x^8)`, we need to only do
`√(8)` which is 4, so answer is
`x^4`.

then divide
`(x^2)/(x^4)` , minus 2 - 4= -2,
`x^-2`

but if there was any negative exponent in math it needs to be down so answer is
`(1)/(x^2)`.