Multiplying Exponents - Math Steps, Examples & Questions

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Math resources Algebra Laws of exponents

Multiplying exponents

Here you will learn about multiplying exponents, including how to apply the properties of exponents when multiplying exponents with the same base and with different bases.

Students will first learn about multiplying exponents as a part of expressions and equations in $katex is not defined$ th grade math and will expand on that knowledge into high school.

What is multiplying exponents?

Multiplying exponents is where you multiply terms that involve exponents, indices or powers. You can multiply exponents in various forms, including whole numbers, negative numbers, fractions, and decimals. There are two methods to multiply terms involving exponents,

When the bases are the same, add the exponents.

For example,

$katex is not defined$

These questions usually ask to ‘simplify’ the calculation.
When the bases are different, multiply the coefficients and keep the exponent the same.

For example,

$katex is not defined$

These questions usually ask to ‘evaluate’ the calculation.

What is multiplying exponents?

[FREE] Multiplying Exponents Worksheet (Grade 8)

Use this worksheet to check your 8th grade students’ understanding of multiplying exponents. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

[FREE] Multiplying Exponents Worksheet (Grade 8)

Use this worksheet to check your 8th grade students’ understanding of multiplying exponents. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

Multiplying exponents when the bases are the same

In order to multiply exponents when the bases are the same, you can use one of the laws of exponents.

When multiplying exponents with the same base, add the powers.

$katex is not defined$

For example,

To simplify the following expression,

$katex is not defined$

Write out each power in its expanded form.

$katex is not defined$

Is there a quicker way to work this out?

Simplifying

$katex is not defined$ to $katex is not defined$

work out the simplified answer as,

$katex is not defined$

The base has stayed the same and you have added the exponents together.

This is the multiplication law of exponents.

Multiplying exponents when the bases are different

When multiplying exponents with different bases, multiply the coefficients and keep the exponent the same.

$katex is not defined$

For example,

To evaluate the following expression:

$katex is not defined$

Write each term of the calculation without using exponential notation. The exponent will tell you the number of times to represent the term.

$katex is not defined$

Work out the final answer by multiplying these numbers together.

$katex is not defined$

Common Core State Standards

How does this relate to $katex is not defined$ th grade math?

Grade 8: Expressions and Equations (8.EE.A.1)
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
For example, $katex is not defined$

How to multiply exponents with the same base

In order to multiply exponents with different bases:

Add the exponents.
Multiply any coefficients.

Multiplying exponents examples

Example 1: exponents with the same base, different exponents

Simplify and leave your answer in exponential form.

$katex is not defined$

Add the exponents.

$katex is not defined$

2Multiply any coefficients.

The coefficients are both $katex is not defined$

The answer is $katex is not defined$

Example 2: bases have a coefficient greater than 1.

Simplify and leave your answer in index form.

$katex is not defined$

Add the exponents.

Add together the exponents $katex is not defined$ and $katex is not defined$

$katex is not defined$

Multiply any coefficients.

Multiply $katex is not defined$ and $katex is not defined$ together.

$katex is not defined$

The answer is $katex is not defined$

Example 3: with negative exponents

Simplify and leave your answer in index form.

$katex is not defined$

Add the exponents.

Add together the exponents $katex is not defined$ and $katex is not defined$

$katex is not defined$

Multiply any coefficients.

Multiply the $katex is not defined$ and $katex is not defined$ together.

$katex is not defined$

How to multiply exponents when the bases are different

In order to multiply exponents with different bases:

Write out each term without the exponents.
Work out the calculation.

Example 4: with positive exponents

Evaluate:

$katex is not defined$

Write out each term without the exponents.

$katex is not defined$

Work out the calculation.

$katex is not defined$

So,

$katex is not defined$

Example 5: with negative exponents

Evaluate:

$katex is not defined$

Write out each term without the exponents.

When multiplying with a negative exponent, like $katex is not defined$ you will find the reciprocal of the term.

$katex is not defined$

Work out the calculation.

$katex is not defined$

So,

$katex is not defined$

Example 6: with three terms

Evaluate:

$katex is not defined$

Write out each term without the exponents.

$katex is not defined$

Work out the calculation.

$katex is not defined$

So,

$katex is not defined$

Teaching tips for multiplying exponents

Before introducing multiplying exponents, students should be able to simplify expressions with the same base, understand the product rule, the power of a power rule, and the other exponent rules.

Introduce students to real-life scenarios that use multiplying exponents, including scientific notation and compound interest.

Provide worksheets with a range of different types of problems on various levels, including negative exponents, fractions as exponents, and mixed expressions.

Easy mistakes to make

Using the multiplying exponents law with terms with different bases
For example,
You cannot simplify $katex is not defined$ as the bases are different.

Confusing exponents and fractional powers
Raising a term to the power of $katex is not defined$ means square it.
For example,
$katex is not defined$

Raising a term to the power of $katex is not defined$ means find the square root of it.
For example,
$katex is not defined$

Raising a term to the power of $katex is not defined$ means cube it.
For example,
$katex is not defined$

Raising a term to the power of $katex is not defined$ means find the cube root of it.
For example,
$katex is not defined$

Practice multiplying exponents questions

katex is not defined

katex is not defined

katex is not defined

katex is not defined

The product of the coefficients is $katex is not defined$

The base numbers are the same, so add the exponents.

$katex is not defined$

The answer is $katex is not defined$

katex is not defined

katex is not defined

katex is not defined

katex is not defined

The product of the coefficients is $katex is not defined$

Because the same base number is the same, add the exponents.

$katex is not defined$

The answer is $katex is not defined$

katex is not defined

katex is not defined

katex is not defined

katex is not defined

The product of the coefficients is $katex is not defined$

Because the base is the same number, add the index numbers.

$katex is not defined$

The correct answer is $katex is not defined$

katex is not defined

katex is not defined

katex is not defined

katex is not defined

As the base numbers are different, evaluate each term and then multiply,

$katex is not defined$

katex is not defined

katex is not defined

katex is not defined

katex is not defined

As the base numbers are different, evaluate each term and then multiply,

$katex is not defined$

katex is not defined

katex is not defined

katex is not defined

katex is not defined

As the base numbers are different, evaluate each term and then multiply,

$katex is not defined$

Multiplying exponents FAQs

What is an exponent?

An exponent is a small number that is written above and to the right of a number, known as the base number. This indicates how many times a number is multiplied by itself (repeated multiplication). For example, $katex is not defined$ read as $katex is not defined$ to the third power, $katex is not defined$ is the base number and $katex is not defined$ is the exponent.

Can you multiply exponents that are fractions or decimals?

Yes, you can still apply the rules of exponents when dealing with exponential expressions that involve decimal or fractional exponents. For example, $katex is not defined$ You would find a common denominator, if needed, and then add the numerators similarly to adding fractions.

What is the power of a power property?

To find a power of a power, you will multiply powers, or multiply the exponents. For example, $katex is not defined$

What is the rule for dividing with exponents?

When dividing exponents with the same base, subtract the powers to calculate the quotient. For example, $katex is not defined$

The next lessons are

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