Math

Treating a Negative Exponent as a Negative Number

Students read a negative exponent like 3−23^{-2} as a negative value and write 3−2=−93^{-2} = -9.

Quick check

Why students make it

The negative sign in the exponent looks like it should make the whole number negative. Students mix up changing sign with taking a reciprocal.

The rule done right

A negative exponent means take the reciprocal of the base with a positive exponent. For any nonzero number aa, a−n=1ana^{-n} = \frac{1}{a^n}.

Related resources

exponentsnegative-exponentsreciprocals