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) }](https://img.qammunity.org/2024/formulas/mathematics/high-school/fwz3u0lw9u4vpemy3y2c735415hdihjvry.png)
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