Free Printable Law of indices

1.

$2^2\div\sqrt[]{16}$

a)

4

b)

$1$

c)

$\frac{1}{8}$

d)

$\frac{1}{2}$

2.

$\left(2^2\times3^3\right)^2$

a)

$2^4\times3^5$

b)

$3^6\times2^4$

c)

$3^3\times2^4$

d)

$2^2\times3^6$

3.

$\frac{3^2}{4^3}\times\frac{2^2}{6}$

a)

$\frac{3}{2}$

b)

$\frac{3}{6^3}$

c)

$\frac{3^2}{2^3}$

d)

$\frac{3}{2^5}$

4.

$\frac{9x^2}{3x}$

a)

$3x$

b)

$9x$

c)

$3x^2$

d)

$\frac{9}{x}$

5.

Consider that

$a^2\times a^{-3}$

$=a^2\times\frac{1}{a^3}$

$=\frac{a^2}{a^3}$

$=\frac{1}{a}$ ,

which of the following rule is used ?

a)

$a^m\cdot a^n=a^{m+n}$

b)

$\left(a^m\right)^n=a^{mn}$

c)

$a^0=1$

d)

$a^{-m}=\frac{1}{a^m}$

6.

For leaving only possitive indices, which is the expression for $a^{-2}$ .

a)

$\frac{1}{a^{ }}$

b)

$\frac{1}{a^{-2}}$

c)

$\frac{1}{a^2}$

d)

$-a^2$

7.

$4^2\cdot4^{-3}$

a)

4

b)

$\frac{1}{4}$

c)

$4^5$

d)

$4^{-5}$

8.

$\frac{1}{2^{-1}}\cdot4$

a)

$2$

b)

$8$

c)

$2^{-1}$

d)

$8^{-1}$

9.

$\frac{3^2}{3^{-2}}$

a)

$3^4$

b)

$3^1$

c)

$3^{-1}$

d)

$1$

10.

Challenge question:

$a^{-1}\cdot a^2\cdot a^{-3}\cdot a^4\cdot\cdot\cdot a^{-9}\cdot a^{10}$

a)

$a^{55}$

b)

$a^5$

c)

$a^{-5}$

d)

$a^{-55}$

Law of indices

Total questions: 10

Worksheet time: 3600secs

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