Free Printable Easy to difficult index laws

1.

Simplify the following: a³ x a⁵

a)

a⁵

b)

a¹⁵

c)

a⁸

d)

1

2.

Simplify the following: w⁰ x w⁰

a)

w¹

b)

1

c)

0

3.

Simplify the following: a⁰ + a⁰

a)

a⁰

b)

2a⁰

c)

1

d)

2

4.

Simplify: (b⁴ x c²) ÷ b³

a)

bc⁸

b)

cb⁸

c)

bc²

d)

cb²

5.

Simplify:
$\left(3ab^2\right)\left(-2b^{-3}\right)$

a)

$-\frac{6a}{b}$

b)

$-\frac{6a^2}{b}$

c)

$ab$

d)

$\frac{3a}{2b}$

6.

What is the value of (-2)³?

a)

-8

b)

-6

c)

6

d)

8

7.

(10³)⁶

a)

10¹⁸

b)

30⁶

c)

10⁹

d)

30³

8.

c³ ÷ c⁷

a)

c⁴

b)

c^-4

c)

c¹³

d)

c^-2

9.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

10.

$d^{\frac{1}{2}}=$

a)

$\sqrt{\left(d^1\right)}$

b)

$\left(d^2\right)^{-1}$

c)

$\left(d^1\right)^{-2}$

d)

$\sqrt{d^2}$

11.

$\left(\sqrt{9x^4y^3}\right)^3=$

a)

$\left(3x^2\right)^3\left(y^9\right)^{\frac{1}{2}}$

b)

$27x^7\left(\sqrt{y}\right)^9$

c)

$27x^6y^{\frac{9}{2}}$

d)

$3x^6y^{\frac{2}{9}}$

12.

Solve $2^{\left(x+1\right)}\times4^{\left(2x-3\right)}=16^{\left(3x-2\right)}$

a)

$\frac{7}{3}$

b)

$\frac{3}{7}$

c)

$-\frac{7}{3}$

d)

$-\frac{3}{7}$

e)

$\frac{4}{7}$

13.

Solve $\left(-9\right)^{\left(1-2x\right)}=3^{-4}$

a)

$\frac{2}{3}$

b)

$-\frac{2}{3}$

c)

$\frac{3}{2}$

d)

$0.3$

e)

$-\frac{3}{2}$

14.

Solve $x^{\frac{1}{4}}=32x^{\frac{7}{8}}$

a)

$-2$

b)

2

c)

$-\frac{1}{2}$

d)

3

e)

$\frac{1}{2}$

15.

$3^{\left(x+2\right)}=3\left(24+3^{\left(x-1\right)}\right)$

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$-2$

d)

2

e)

$\frac{3}{2}$

Easy to difficult index laws

Total questions: 15

Worksheet time: 34mins

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