Question

Express each of the following in power notation:

(i) $\frac{25}{36}$
(ii) $\frac{-27}{64}$
(iii) $\frac{-32}{243}$
(iv) $\frac{-1}{128}$

Answer 1

(i) $\frac{25}{36}=\frac{5^2}{6^2}$ [since 25 = 5² and 36 = 6²]
$={\left(\frac{5}{6}\right)}^2$

(ii) $\frac{-27}{64}=\frac{{\left(-3\right)}^3}{4^3}$ [since −27 = (−3)³ and 64 = 4³]

$={\left(\frac{-3}{4}\right)}^3$

(iii) $\frac{-32}{243}=\frac{{\left(-2\right)}^5}{3^5}$ [since −32 = (−2)⁵ and 243 = 3⁵]
$={\left(\frac{-2}{3}\right)}^5$

(iv) $\frac{-1}{128}=\frac{{\left(-1\right)}^7}{2^7}$ [since (−1)⁷ = −1 and 128 = 2⁷]
$={\left(\frac{-1}{2}\right)}^7$