Negative exponents

Statement

Write without negative exponents: (a) $(-3)^{-2}$; (b) $\dfrac{1}{5^{-2}}$; (c) $\dfrac{4^{-1}\,s^{-2}\,t^{3}}{t^{6}}$.

Solution

Recall that $a^{-n} = \dfrac{1}{a^n}$ (with $a\neq 0$).

(a) $(-3)^{-2} = \dfrac{1}{(-3)^2} = \dfrac{1}{9}.$

(b) $\dfrac{1}{5^{-2}} = 5^{2} = 25.$

(c) Move the factors with negative exponent to the right place: $\frac{4^{-1}\,s^{-2}\,t^{3}}{t^{6}} = \frac{t^{3}}{4\,s^{2}\,t^{6}} = \frac{1}{4\,s^{2}\,t^{3}}.$

$\boxed{\tfrac{1}{9} \ ;\quad 25 \ ;\quad \dfrac{1}{4s^2 t^3}}$