Division Rules for Exponents

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• Division Rules for Exponents

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Division Rules of Exponents Essential Questions

• How do I divide powers with the same bases?
• How do I simplify expressions with negative and
  zero exponents?

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Rules and Properties

• Quotient-of-Powers Property
• For all nonzero real numbers x and all integers m
  and n, where m gt n,

When dividing like bases, subtract the exponents.
1.
Examples
x2

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Examples

• Use the properties of exponents to simplify
  expressions containing fractions.

Subtract the exponents for the x (7 -1 6)
2.
x6y

Subtract the exponents for the y (3 -2 1)
Reduce the coefficients.
2x3
4x5
3.

6x2
3
Subtract the exponent of the variables.
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Do These Together
x6
4.
x2
x4
x3y7
5.
x2y3
xy4
x4y2z2
5x7y3z6
6.

3
15x3yz4
10x3y4
5x2

7.
3
6xy4
6
TRY THESE
x8
8.
x5
x3
x4y7
9.
y5
x4y2
3x2y3z3
6x4y6z8
10.

2x2y3z5
18x5y9
3x2y6

11.
2
12x3y3
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Zero Exponents
By applying the product of powers property to the
following example, we find that
Zero Property of Exponents A nonzero number to
the zero power is 1
We can then divide both sides of the equation by
37 to determine the value of 30
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Examples
Evaluate the following expressions.
Solutions
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Negative Exponents
By applying the product of powers property to the
following example, we find that
We can then divide both sides of the equation by
an to determine the value of a-n
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Rewrite the following expressions using positive
exponents.
Evaluate the following expressions.
Solutions
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1. Evaluate the following expressions.

1. Rewrite the following expressions with positive
   exponents.

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