# Test: Indices II - Challenging

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Question 1:   Calculate: $81×{\left(-3\right)}^{-5}$
$-\frac{1}{9}$
$\frac{1}{9}$
$-\frac{1}{3}$ 
$\frac{1}{3}$
Question 2:   Calculate: ${32}^{0}+{2}^{-1}$
$1\frac{1}{2}$
$30$
$34$
$-1\frac{1}{2}$
Question 3:   Calculate: $\frac{{724}^{2}-{76}^{2}}{324}$
$1600$
$160$
$-160$
$-1600$
Question 4:   Simplify expression: ${\left(-2{x}^{4}y\right)}^{3}{\left(-0.5x{y}^{5}\right)}^{2}$
 $-2{x}^{14}{y}^{13}$
$2{x}^{14}{y}^{13}$
${x}^{14}{y}^{13}$
$-{x}^{14}{y}^{13}$
Question 5:   Find value of p: ${p}^{5}={2}^{25}$
$20$
$25$
$2$
$32$
Question 6:   Calculate: ${100}^{-2}:{0.1}^{4}+\frac{2}{5}$
$1\frac{2}{5}$
$\frac{2}{5}$
$100$
$1$
Question 7:   Calculate: ${0.5}^{2}:{\left(\frac{1}{4}\right)}^{-2}×{\left(\frac{1}{2}\right)}^{-6}$ 
$-10$
$10$
$1$
-1$-1$
Question 8:   Write in a standard form: $8902.5$
$8.9025×{10}^{3}$
$89.025×{10}^{3}$
$8.9025$
$89025$
Question 9:   Calculate: $1.8×{10}^{4}+5×{10}^{3}$
$2.3×{10}^{7}$
$6.8×{10}^{7}$
$23000$
$2200$
Question 10:   Solve the equation: $3{x}^{-1}+{x}^{-1}=1$
$3$
$1$
$0$
$4$