Exponents 8 – Negative Exponents

Table of Contents

• Negative Exponents
  • Negative Exponent as Positive Exponent
  • Positive Exponent as Negative Exponent
• Summary
• What’s Next?

In the previous segment, we learnt what Exponents are. In this segment, we will learn about Negative Exponents.

What are Negative exponents?

When the power of a given number is negative, it is a negative exponent.

For example,

Consider 13⁻⁴. Here, the base is 13 and -4 is the negative exponent.

How to express a negative exponent as a positive exponent?

A negative exponent can be expressed as a positive exponent in the form of a fraction whose numerator is 1 and the denominator is a number formed by changing the sign of the exponent.

That is, ?^−? = 1

??

, ?ℎ???? ≠ 0.

For example,

3−4 = 3−4 × 34

34

= 3−4×34

34

= 3−4+4

34

=30

34

= 1

34

∴ 3⁻⁴ = 1

34