Free Printable Index Law 4 and 5

1.

(4a)²=

a)

4a²

b)

16a²

c)

8a²

d)

8a

2.

Simplify the following: (3ab⁴)³

a)

9a³b¹²

b)

9a³b⁷

c)

27a³b¹²

d)

27a³b⁷

e)

3³a³b¹²

3.

Simplify (2 x 3³)³

a)

2³ x 3⁹

b)

2³ x 3⁶

c)

2⁴ x 3⁹

4.

$Simplify\ \ \ \left(\frac{x^4}{y^5}\right)^3$

a)

$\frac{x^7}{y^8}$

b)

$\frac{x^{12}}{y^{10}}$

c)

$\frac{x^{15}}{y^{12}}$

d)

$\frac{x^{12}}{y^{15}}$

5.

Simplify $\left(\frac{4v^7}{2v}\right)^2$

a)

$4v^{14}$

b)

$4v^{12}$

c)

$16v^{14}$

d)

$16v^{12}$

6.

Simplify: (3h²)³

a)

27h⁶

b)

27h⁵

c)

9h⁶

d)

9h⁵

7.

Simplify: (2x²y)² × (3xy³)⁰

a)

4x⁴y²

b)

12x⁴y²

c)

4x⁵y⁵

d)

12x⁵y⁵

8.

Simplify the following: a⁰ + a⁰

a)

a⁰

b)

2a⁰

c)

1

d)

2

9.

$Simplify\ \ \ \ \left(p^2\right)^4\times\left(q^4\right)^5$

a)

$p^8q^{20}$

b)

$p^6q^9$

c)

$p^{24}q^{45}$

d)

$p^8q^{15}$

10.

$Simplify\ \ \ \ \left(2z^4\right)^3\times\left(3y^7\right)^2$

a)

$6z^7y^9$

b)

$6z^{12}y^{14}$

c)

$72z^7y^9$

d)

$72z^{12}y^{14}$

11.

Simplify $\left(\frac{4v^7}{2v}\right)^2$

a)

$4v^{14}$

b)

$4v^{12}$

c)

$16v^{14}$

d)

$16v^{12}$

12.

$Simplify\ \left(5x^4y^6\right)^3$

a)

$5x^{12}y^{18}$

b)

$125x^{12}y^{18}$

c)

$5x^7y^9$

d)

$125x^7y^9$

13.

Expand and simplify: (3m²4n³)²

a)

144m⁴n⁶

b)

12m⁴n⁶

c)

24m⁴n⁵

d)

12m²n⁵

14.

a⁵b¹⁰/ a³b³

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

15.

Simplify the following

\frac{26x^7y^4}{13x^2y^3}

a)

$13x^5y$

b)

$2x^5y^3$

c)

$13x^1y^5$

d)

$2x^5y$

Index Law 4 and 5

Total questions: 15

Worksheet time: 15mins

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