# How to Multiply 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: $$x^a×x^b=x^{\ a+b}$$, $$\frac{x^a}{x^{b}} =x^{\ a-b}$$
$$(x^{a})^{b}=x^{ \ a×b}$$, $$(xy)^{a}=x^{a}×y^{a} , (\frac{a}{b})^{c}=\frac{a^{c}}{b^{c}}$$

### Multiplication Property of Exponents – 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: $$4x^3×2x^2=8x^5$$

### Multiplication Property of Exponents – Example 2:

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

Solution:

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

### Multiplication Property of Exponents – 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: $$-2x^5×7x^3=-14x^8$$

### Multiplication Property of Exponents – 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 for Multiplying Property of Exponents

### 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. $$\color{blue}{3x^5y^3 . 8x^2y^3}$$

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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