Multiplication Property of Exponents

Multiplication Property of Exponents

Learn how to multiply exponents by using multiplication property of exponents in a few simple steps.

Step by step guide to multiply exponents

  • Exponents are shorthand for repeated multiplication of the same number by itself. For example, instead of \(2×2\), we can write \(2^ {\color{blue}{2}} \). For \(3×3×3×3\), we can write \(3^{\color{blue}{4}}\)
  • In algebra, a variable is a letter used to stand for a number. The most common letters are: \(x,y,z,a,b,c,m\),and \(n\).
  • Exponent’s rules: \(x^a×x^b=x^{\ a+b}\), \(\frac{x^a}{x^{b}} =x^{\ a-b}\)
    \((x^{a})^{b}=x^{ \ a×b}\), \((xy)^{a}=x^{a}×y^{a} , (\frac{a}{b})^{c}=\frac{a^{c}}{b^{c}} \)

Example 1:

Multiply \(4x^3 \times 2x^2=\)

Solution:

Use Exponent’s rules: \(\color{blue}{x^a×x^b=x^{a+b} }→x^3×x^2=x^{3+2}=x^5\)
Then: \(4x^3×2x^2=8x^5 \)

Example 2:

Multiply \((x^3 y^5 )^2= \)

Solution:

Use Exponent’s rules: \(\color{blue}{(x^a)^{b}=x^{a×b}}\). Then: \((x^3 y^5 )^2=x^{3×2} y^{5×2}=x^6 y^{10} \)

Example 3:

Multiply. \(-2x^5×7x^3=\)

Solution:

Use Exponent’s rules: \(\color{blue}{x^a×x^b=x^{a+b} } →x^5×x^3=x^{5+3}=x^8\)
Then: \(-2x^5×7x^3=-14x^8 \)

Example 4:

Multiply. \((x^2 y^4 )^3= \)

Solution:

Use Exponent’s rules: \(\color{blue}{(x^a)^{b}=x^{a×b}} \). Then: \((x^2 y^4 )^3=x^{2×3} y^{4×3}=x^6 y^{12} \)

Exercises

Simplify.

  1. \(\color{blue}{6x. 2x^2}\)
  2. \(\color{blue}{5x^4 . 5x^4}\)
  3. \(\color{blue}{6x^2 . 6x^3y^4}\)
  4. \(\color{blue}{7x^2y^5 . 9xy^3}\)
  5. \(\color{blue}{7xy^4 . 4x^3y^3}\)
  6. \(\color{blue}{3x^5y^3 . 8x^2y^3}\)

Download Multiplication Property of Exponents Worksheet

  1. \(\color{blue}{12x^3}\)
  2. \(\color{blue}{25x^8}\)
  3. \(\color{blue}{36x^5y^4}\)
  4. \(\color{blue}{63x^3y^8}\)
  5. \(\color{blue}{28x^4y^7}\)
  6. \(\color{blue}{24x^7y^6}\)

Related to "Multiplication Property of Exponents"

Top 10 Grade 8 PARCC Math Practice Questions
Top 10 Grade 8 PARCC Math Practice Questions
FREE Grade 7 PARCC Math Practice Test
FREE Grade 7 PARCC Math Practice Test
Grade 6 STAAR Math Worksheets
Grade 6 STAAR Math Worksheets
Top 10 Grade 7 ACT Aspire Math Practice Questions
Top 10 Grade 7 ACT Aspire Math Practice Questions
TExES Core Math FREE Sample Practice Questions
TExES Core Math FREE Sample Practice Questions
Grade 6 PSSA Math Worksheets
Grade 6 PSSA Math Worksheets
FREE Grade 7 SBAC Math Practice Test
FREE Grade 7 SBAC Math Practice Test
ATI TEAS 6 Math Practice Test Questions
ATI TEAS 6 Math Practice Test Questions
Top 10 Grade 8 Georgia Milestones Assessment System Math Practice Questions
Top 10 Grade 8 Georgia Milestones Assessment System Math Practice Questions
SHSAT Math FREE Sample Practice Questions
SHSAT Math FREE Sample Practice Questions

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…