Question

Write the proper numbers in the boxes.

(1) ${\left(\frac{4}{11}\right)}^6=\frac{4^{\boxed{}}}{{11}^{\boxed{}}}$
(2) ${\left(\frac{-5}{17}\right)}^3=\frac{{\left(-5\right)}^{\boxed{}}}{{17}^{\boxed{}}}$
(3) ${\left(\frac{1}{10}\right)}^{20}=\frac{1}{{10}^{\boxed{}}}$
(4) ${\left(\frac{a}{b}\right)}^2=\frac{a^{\boxed{}}}{b^{\boxed{}}}$
(5) ${\left(\frac{6}{7}\right)}^3=\frac{6^{\boxed{}}}{7^{\boxed{}}}$
(6) ${\left(\frac{5}{7}\right)}^8=\frac{5^{\boxed{}}}{7^{\boxed{}}}$
(7) ${\left(\frac{x}{y}\right)}^7=\frac{x^{\boxed{}}}{y^{\boxed{}}}$
(8) ${\left(\frac{1}{5}\right)}^3=\frac{1^{\boxed{}}}{5^{\boxed{}}}$

Answer 1

(1) ${\left(\frac{4}{11}\right)}^6=\frac{4^{\boxed{}}}{{11}^{\boxed{}}}$
Consider ${\left(\frac{4}{11}\right)}^6$
$=\frac{4^{\boxed{6}}}{{11}^{\boxed{6}}}\left[{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}\right]$

(2) ${\left(\frac{-5}{17}\right)}^3=\frac{{\left(-5\right)}^{\boxed{}}}{{17}^{\boxed{}}}$
Consider ${\left(\frac{-5}{17}\right)}^3$
$=\frac{{\left(-5\right)}^{\boxed{3}}}{{17}^{\boxed{3}}}\left[{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}\right]$

(3) ${\left(\frac{1}{10}\right)}^{20}=\frac{1^{\boxed{}}}{{10}^{\boxed{}}}$
Consider ${\left(\frac{1}{10}\right)}^{20}$
$$\begin{gathered} =\frac{1^{20}}{{10}^{20}}\left[{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}\right] \\ =\frac{1}{{10}^{\boxed{20}}} \end{gathered}$$

(4) ${\left(\frac{a}{b}\right)}^2=\frac{a^{\boxed{}}}{b^{\boxed{}}}$
Consider ${\left(\frac{a}{b}\right)}^2$
$=\frac{a^{\boxed{2}}}{b^{\boxed{2}}}\left[{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}\right]$

(5) ${\left(\frac{6}{7}\right)}^3=\frac{6^{\boxed{}}}{7^{\boxed{}}}$
Consider${\left(\frac{6}{7}\right)}^3$
$=\frac{6^{\boxed{3}}}{7^{\boxed{3}}}\left[{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}\right]$

(6) ${\left(\frac{5}{7}\right)}^8=\frac{5^{\boxed{}}}{7^{\boxed{}}}$
Consider ${\left(\frac{5}{7}\right)}^8$
$=\frac{5^{\boxed{8}}}{7^{\boxed{8}}}\left[{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}\right]$

(7) ${\left(\frac{x}{y}\right)}^7=\frac{x^{\boxed{}}}{y^{\boxed{}}}$
Consider ${\left(\frac{x}{y}\right)}^7$
$=\frac{x^{\boxed{7}}}{y^{\boxed{7}}}\left[{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}\right]$

(8) ${\left(\frac{1}{5}\right)}^3=\frac{1^{\boxed{}}}{5^{\boxed{}}}$
Consider${\left(\frac{1}{5}\right)}^3$
$=\frac{1^{\boxed{3}}}{5^{\boxed{3}}}\left[{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}\right]$