Free Printable Indices

1.

Write 6 x 6 x 6 in index notation.

a)

$6^3$

b)

$6^6$

c)

$6^{18}$

d)

$6^2$

2.

Write 15 x 15 x 15 x 15 x 15 x 15 x 15 in index notation.

a)

$15^{15}$

b)

$15^7$

c)

$15^5$

d)

$7^{15}$

3.

Write s x s x s x s in index notation.

a)

$s^1$

b)

$s^2$

c)

$s^3$

d)

$s^4$

4.

Write j x j x j x j x j x j x j x j x j x j in index notation.

a)

$j^9$

b)

$j^j$

c)

$j^{10}$

d)

$j^8$

5.

Write $3^5$ as a product of prime factors.

a)

3 x 5 x 3 x 5

b)

5 x 5 x 5

c)

3 x 3 x 3 x 3

d)

3 x 3 x 3 x 3 x 3

6.

Write $b^7$ as a product of prime factors.

a)

b x b x b x b x b x b x b

b)

b x 7 x b x 7 x b x 7 x b

c)

7 x 7 x 7 x 7 x 7 x 7 x 7

d)

7b x 7b x 7b x 7b x 7b x 7b x 7b

7.

Write 8 x 8 in index form using 2 as the base.

a)

$2^2\ \ \times\ \ 4^2$

b)

2 x 4 x 2 x 4

c)

$2^6$

d)

2 x 2 x 2 x 2 x 2 x 2

8.

Write 9 x 9 in index form using 3 as the base.

a)

3 x 3 x 3 x 3

b)

$3^4$

c)

$9^2$

d)

3 x 9 x 3 x 9

9.

Challenging Question

Write 625 in index form using 5 as the base.

a)

25 x 25

b)

$5^4$

c)

5 x 5 x 5 x 5

d)

$25^2$

10.

Express $w^{-5}$ as a positive index.

a)

5w x 5w x 5w x 5w x 5w

b)

w x w x w x w x w

c)

$\frac{1}{5^w}$

d)

$\frac{1}{w^5}$

11.

Express $4\ a^{-6}$ as a positive index.

a)

4a x 4a x 4a x 4a x 4a x 4a

b)

$\frac{4}{a^{-6}}$

c)

$\frac{4}{a^6}$

d)

4 x a x a x a x a x a x a

12.

Express $9^{-2}\ \ h^{-7}$ as a positive index.

a)

$\frac{1}{9^2\ h^7}$

b)

$\frac{1}{9^{-2}\ \ h^{-7}}$

c)

$\frac{9^2}{h^7}$

d)

$\frac{h^7}{9^2}$

13.

Simplify $3^2\ \ \times\ \ 3^{-7}$ as positive index.

a)

$3^5$

b)

$\frac{1}{3^5}$

c)

$\frac{1}{3^{-5}}$

d)

$3^{-5}$

14.

Simplify $f^{-4}\ \times\ \ f^5$ as positive index.

a)

$\frac{f^5}{f^4}$

b)

$\frac{f^{-4}}{f^5}$

c)

$f^{-1}$

d)

$f$

15.

Simplify and express $6^{3\ }\div\ 6^5$ in positive index form.

a)

$6^2$

b)

$\frac{6\ \ \times\ \ 6\ \ \times\ \ 6}{6\ \ \times\ \ 6\ \ \times\ \ 6\ \ \times\ \ 6\ \ \times\ \ 6}$

c)

$6^{-2}$

d)

$\frac{1}{6^2}$

16.

Simplify and express $y^8\ \ \div\ \ y^2$ in positive index form.

a)

$y^6$

b)

$y^{-6}$

c)

$\frac{1}{y^6}$

d)

$\frac{1}{y^{-6}}$

17.

Simplify and express $\left(10^2\right)^{-1}$ as a positive index.

a)

$10^{-2}$

b)

$10^2$

c)

$\frac{1}{10^2}$

d)

$\frac{1}{10^{-2}}$

18.

Simplify and express $\left(x^{-2}\right)^5$ as positive index.

a)

$x^{10}$

b)

$x^{-10}$

c)

$\frac{1}{x^{10}}$

d)

$\frac{1}{x^{-10}}$

19.

Simplify and express $5\ \left(n^2\right)^{-3}$ as positive index.

a)

$\frac{5}{n^6}$

b)

$5\ \ \times\ \ n^6$

c)

$5\ \ \times\ \ n^{-6}$

d)

$\frac{n^6}{5}$

20.

Simplify and express $10\ \left(q^{-5}\right)^3$ as a positive index.

a)

$10\ \times\ q^{-15}$

b)

$10\ \ \times\ \ q^{15}$

c)

$\frac{10}{q^{15}}$

d)

$\frac{10}{q^{-15}}$

Indices

Total questions: 20

Worksheet time: 3600secs

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