Free Printable Index Laws 4,5 &6 and Negative Indices

1.

Simplify the following expression

$\left(v^3\right)^5$

a)

$v^{35}$

b)

$v^8$

c)

$v^{15}$

d)

$v^{-2}$

2.

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

a)

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

b)

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

c)

$15x^{12}y^{18}$

d)

$15x^7y^9$

3.

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

a)

$p^8q^{20}$

b)

$p^6q^9$

c)

$\left(pq\right)^{80}$

4.

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

a)

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

b)

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

c)

$72z^7y^9$

5.

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

a)

$\left(\frac{x^{34}}{y^{35}}\right)$

b)

$\left(\frac{x^7}{y^8}\right)$

c)

$\left(\frac{x^{12}}{y^{15}}\right)$

6.

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

a)

$2v^{12}$

b)

$4v^{12}$

c)

$4v^6$

d)

$2v^6$

7.

Simplify the following to give a positive index $g^{-5}$

a)

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

b)

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

c)

$\frac{1}{5g}$

d)

$\frac{g}{5}$

8.

Simplify to give a positive indice $\ 2x^{-9}\times8x^4$

a)

$16x^{-5}$

b)

$\frac{16}{x^5}$

c)

$\frac{28}{x^5}$

d)

$\frac{16}{x^{36}}$

9.

Simplify to give a positive indices $\left(s^5z^3\right)^{-4}$

a)

$s^{20}z^{12}$

b)

$\frac{1}{s^{20}z^{12}}$

c)

$\frac{s}{z}$

10.

Simplify to give positive indices

\frac{y^5}{y^9}

a)

$\frac{1}{y^4}$

b)

$y^{-4}$

c)

$y^4$

11.

Simplify to give positive indices

\frac{2a^4b^6c}{a^2b^8c^3}

a)

$2a^2b^2c^2$

b)

$2a^2b^{-2}c^{-2}$

c)

$\frac{2a^2}{b^2c^2}$

d)

$\frac{2}{a^2b^2c^2}$

Index Laws 4,5 &6 and Negative Indices

Total questions: 11

Worksheet time: 6mins

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