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. \(\color{blue}{24x^7y^6}\)

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