Quotient rule of exponents

Quotient rule simply states that as long as the base is the same, we can just divide two powers by subtracting the exponents. This is a shortcut to simplify exponents.

Basic concepts:
Using exponents to describe numbers
Exponent rules
Order of operations with exponents

Related concepts:
Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$
Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$
Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$
Exponents: Negative exponents

Lessons

Notes:

$\frac{a^m}{b^n}$ = ${ a^{m-n}}$

2.
Simplify the following:

Quotient rule of exponents

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Using exponents to describe numbers

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Order of operations with exponents

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Notes:

ambn \frac{a^m}{b^n} ​b​n​​​​a​m​​​​= am−n { a^{m-n}}a​m−n​​

1.

What are exponent rules?

2.

Simplify the following:

a)

a9a5 \frac{a^9}{a^5}​a​5​​​​a​9​​​​

b)

x11y6z3x3y2z2 \frac{x^{11}y^6z^3}{x^3y^2z^2}​x​3​​y​2​​z​2​​​​x​11​​y​6​​z​3​​​​

Don't just watch, practice makes perfect.

Quotient rule of exponents

Don't just watch, practice makes perfect.

We have over 1130 practice questions in Basic Algebra for you to master.

Algebra
Using exponents to describe numbers

Algebra
Exponent rules

Algebra
Order of operations with exponents

or

$\frac{a^m}{b^n}$ = ${ a^{m-n}}$

$\frac{a^9}{a^5}$

$\frac{x^{11}y^6z^3}{x^3y^2z^2}$