# Exponents with negative bases

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Videos, worksheets, stories and songs to help Grade 6 students learn about exponents with negative bases.
In this lesson, we will learn how to evaluate negative numbers raise to powers with and without parenthesis.

The following diagram shows how to evaluate exponents with negative bases. Scroll down the page for more examples and solutions.

We can have a negative base raised to a power.
Remember to take note of the parenthesis.
For example,
−24 = −16, (−2)4 = 16

A negative base raised to an even power is positive. A negative base raised to an odd power is negative.
For example,
(−2)4 = 16, (−2)3 = −8

Evaluating Negative Numbers Raised to Powers
This video provides examples of evaluating negative numbers raise to powers with and without parentheses.
Examples:
Evaluate:
(-4)2
-42
(-3)4
-34
(-2)3
-23

Exponents with negative bases and exponents with positive bases
ExamplesL
Simplify:
a. -24
b. (-2)4

Nagative Bases
We can use the rules of the multiplication of negative numbers to determine the sign of a negative base raised to an exponent.
Remember that a negative number times a positive number is a negative number and that two negative numbers multiplied together is a positive number.
When negative bases are raised to odd numbered powers, they give us negative results.
When negative bases are raised to even numbered powers, they give us positive results.

Exponents with Negative Bases
Rules:
In negative base with brackets,
When the exponent is even, the answer is positive and
when the exponent is odd, the answer is negative.

In negative bases without brackets, the answer is always negative
Examples:
-15 + 12
(-2)3 + (-2)2
-2(-2)4 + (-3)3

Evaluate Powers
Learn how to evaluate powers.
Examples:

1. Evaluate.
a) 34
b) -112
c) (-7)3
2. Express 81 in powers of 3.

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