Test: Indices - Challenging

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Question 1:   Solve: $\frac{\sqrt{{4}^{2}+{3}^{2}}}{\sqrt{{5}^{2}}}$
$1\frac{2}{5}$
$1$
$0$
$1\frac{3}{5}$
Question 2:   Solve: ${\left(6\sqrt{3}:2\sqrt{3}\right)}^{2}$
$18$
$3$
$9$
$27$
Question 3:   Solve: $\left(\sqrt{{\left(-5\right)}^{2}}\right)\cdot {\left(-\frac{1}{5}\right)}^{-1}$
$25$
$-25$
$-5$
$5$
Question 4:   Simplify: $\left({x}^{2}+{x}^{3}\right)\left({x}^{4}-{x}^{5}\right)$
$2{x}^{2}+x$ 
${x}^{6}-{x}^{8}$
${x}^{4}$
${x}^{4}-{x}^{3}$
Question 5:   Simplify: $\sqrt{\left(\frac{{x}^{8}}{{x}^{15}}\right)\cdot \left(\frac{{x}^{2}}{{x}^{5}}\right)}$
$\frac{1}{{x}^{5}}$
$\frac{1}{{x}^{3}}$
$\frac{1}{{x}^{2}}$
$\frac{1}{{x}^{10}}$
Question 6:   Solve: ${25}^{\frac{1}{2}}+{16}^{\frac{1}{2}}+{9}^{\frac{1}{2}}-{36}^{\frac{1}{2}}$
$2\sqrt{6}$
$9$
$6$
$5$
Question 7:   Solve: ${\left(\left({27}^{\frac{2}{3}}\cdot {27}^{-\frac{2}{3}}\right)\cdot \left(-1\right)\right)}^{13}$
$1$
$3$
$0$
$-1$
Question 8:   If ${2}^{x}=1024$ , find $x$
$x=8$
$x=12$
$x=6$
$x=10$
Question 9:   If ${6}^{3x+5}={36}^{x+1}$ , find $x$
$x=6$
$x=\frac{1}{3}$
$x=-6$
$x=-3$
Question 10:   If ${2}^{2x-5}-{128}^{x+1}=0$ , find $x$
$x=4$
$x=-2\frac{2}{5}$
$x=-\frac{4}{5}$
$x=13$