Question

Write the proper value in the boxes.

(1) $5^{-10}=\frac{1}{5^{\boxed{}}}$
(2) ${\left(\frac{1}{8}\right)}^{-4}=\frac{1}{{\left({\displaystyle \frac{1}{8}}\right)}^{\boxed{}}}$
(3) ${\left(-4\right)}^{-2}=\frac{1}{{\left(-4\right)}^{\boxed{}}}$
(4) ${12}^{-9}=\frac{1}{{12}^{\boxed{}}}$

Answer 1

(1) $5^{-10}=\frac{1}{5^{\boxed{}}}$
Consider 5⁻¹⁰
$=\frac{1}{5^{\boxed{10}}}\left(a^{-m}=\frac{1}{a^m}\right)$

(2) ${\left(\frac{1}{8}\right)}^{-4}=\frac{1}{{\left({\displaystyle \frac{1}{8}}\right)}^{\boxed{}}}$
Consider ${\left(\frac{1}{8}\right)}^{-4}$
$=\frac{1}{{\left({\displaystyle \frac{1}{8}}\right)}^{\boxed{4}}}\left(a^{-m}=\frac{1}{a^m}\right)$

(3) ${\left(-4\right)}^{-2}=\frac{1}{{\left(-4\right)}^{\boxed{}}}$
Consider (−4)⁻²
$=\frac{1}{{\left(-4\right)}^{\boxed{2}}}\left(a^{-m}=\frac{1}{a^m}\right)$

(4) ${12}^{-9}=\frac{1}{{12}^{\boxed{}}}$
Consider 12⁻⁹
$=\frac{1}{{12}^{\boxed{9}}}\left(a^{-m}=\frac{1}{a^m}\right)$