# Test: Indices - Ambitious

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Question 1:   Find ${100000}^{\frac{1}{5}}$
$10$
$100$
$1$
$2000$
Question 2:   Find ${10}^{0}+{5}^{2}-{27}^{\frac{1}{3}}$
$19$
$23$
$-2$
$16$
Question 3:   Find ${\left({x}^{\frac{1}{2}}\right)}^{-1}\cdot {x}^{\frac{3}{4}}$, if $x=81$
$0$
$3$
$1$
$9$
Question 4:   Find ${\left({x}^{\frac{1}{5}}\right)}^{-2}+3\cdot {\left(\frac{x}{2}\right)}^{-\frac{1}{2}}$, if $x=32$
$\frac{1}{4}$
$1$
$2$
$\frac{1}{2}$
Question 5:   Find the value of $x$ in $\left({4}^{5}\cdot x+{32}^{2}\right)\cdot {2}^{5}={2}^{16}\cdot x$
$-1$
$16$
$8$
$1$
Question 6:   Write in index form: $\sqrt[7]{x}$
${x}^{-\frac{1}{7}}$
${x}^{2}$
${x}^{\frac{1}{7}}$
${x}^{7}$
Question 7:   Write in index form: $\frac{1}{\sqrt[3]{x}}$
${x}^{-\frac{1}{3}}$
${x}^{3}$
${x}^{\frac{2}{3}}$
${x}^{\frac{1}{3}}$
Question 8:   Write in index form: $\sqrt[7]{{x}^{3}}$
${x}^{\frac{3}{7}}$
${x}^{-\frac{7}{3}}$
${x}^{-\frac{3}{7}}$
${x}^{\frac{1}{3}}$
Question 9:   If $y={x}^{\frac{1}{2}}$, solve $x-9{x}^{\frac{1}{2}}+20=0$
$\left\{\begin{array}{l}{x}_{1}=16\\ {x}_{2}=25\end{array}$
$\left\{\begin{array}{l}{x}_{1}=4\\ {x}_{2}=5\end{array}$
$\left\{\begin{array}{l}{x}_{1}=8\\ {x}_{2}=10\end{array}$
$\left\{\begin{array}{l}{x}_{1}=2\\ {x}_{2}=\sqrt{5}\end{array}$
Question 10:   If $y={x}^{\frac{1}{3}}$, solve ${x}^{\frac{1}{3}}-5+6{x}^{-\frac{1}{3}}=0$
$\left\{\begin{array}{l}{x}_{1}=3\\ {x}_{2}=2\end{array}$
$\left\{\begin{array}{l}{x}_{1}=27\\ {x}_{2}=8\end{array}$
$\left\{\begin{array}{l}{x}_{1}=4\\ {x}_{2}=2\end{array}$
$\left\{\begin{array}{l}{x}_{1}=6\\ {x}_{2}=4\end{array}$