QuestionSimplify $\frac{x^{-1}}{x^{8}}$ using exponent properties and show only positive exponents.

Studdy Solution

STEP 1

Assumptions1. The base of the exponent is x. . The numerator has an exponent of -1.
3. The denominator has an exponent of8.
4. We are required to simplify the expression and only include positive exponents.

STEP 2

The rule of exponents states that when we divide like bases, we subtract the exponents. In this case, we subtract the exponent of the denominator from the exponent of the numerator.
$\frac{x^{-1}}{x^{8}} = x^{-1-8}$

STEP 3

Subtract the exponents.
$x^{-1-8} = x^{-9}$

STEP 4

However, we are asked to only include positive exponents. The rule of exponents states that a negative exponent means that the base is on the wrong side of the fraction bar, so it needs to be moved to the other side. In this case, x is in the numerator, so we move it to the denominator.
$x^{-9} = \frac{1}{x^{9}}$ The expression $\frac{x^{-1}}{x^{8}}$ simplifies to $\frac{1}{x^{9}}$ with positive exponents.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms