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

Simplify the given expression. Show all steps. Submit your handwritten work or use-example-1
User Farfarak
by
6.8k points

2 Answers

2 votes

Answer:

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

User Ertebolle
by
7.7k points
3 votes

Answer:


(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).

User Driscoll
by
7.1k points