Exponents 3 – Negative Base

In the previous segment, we looked at the numbers 0 and 1 as bases and exponents.

In this segment, we will learn about Negative base exponents.

Exponents with a negative base

• When a base is a negative number, the result can be either a positive number or a negative number depending upon the exponent.
• If the exponent is even, then the result is positive and if the exponent is odd, then the result is negative.

For example,

(?)(−4)² = (−4) × (−4) = 16

(??)(−4)³ = (−4) × (−4) × (−4) = 16 × (−4) = −64

• Parentheses () plays an important role when the base is negative.

For example,

(-3)4 is not the same as -34.

(−3)⁴ = (−3) × (−3) × (−3) × (−3) = 81

−3⁴ = −3 × 3 × 3 × 3 = −81

Here, (−3)⁴ is a negative base exponent whereas −3⁴ is a positive base exponent.

Summary

Negative Base Exponents

If the exponent of a negative base is even, the result is positive If the exponent of a negative base is odd, the result is negative

What’s next?

In the next segment of Class 7 Maths, we learn about the Product law of exponents.