Question Find the exponent in the equation $\frac{m^{14}}{m^{5}}=m^{?}$ .

Studdy Solution

STEP 1

Assumptions
1. The base $m$ is the same in both the numerator and the denominator.
2. The laws of exponents apply, specifically the quotient rule which states that when dividing like bases, you subtract the exponents.

STEP 2

Apply the quotient rule for exponents which states that when dividing powers with the same base, you subtract the exponents.
$\frac{m^{a}}{m^{b}} = m^{a-b}$

STEP 3

Plug in the given values for the exponents $a$ and $b$ to calculate the exponent of the solution.
$\frac{m^{14}}{m^{5}} = m^{14-5}$

STEP 4

Subtract the exponents.
$m^{14-5} = m^{9}$
The exponent of the solution is 9.

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