Free Printable Index Laws 4-7

1.

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

a)

$v^2$ Simplify

b)

$v^8$

c)

$v^{15}$

d)

$v^{35}$

2.

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

a)

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

b)

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

c)

$5x^7y^9$

d)

$125x^7y^9$

3.

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

a)

$p^8q^{20}$

b)

$p^6q^9$

c)

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

d)

$p^8q^{15}$

4.

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

a)

$6z^7y^9$

b)

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

c)

$72z^7y^9$

d)

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

5.

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

a)

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

b)

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

c)

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

d)

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

6.

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

a)

$4v^{14}$

b)

$4v^{12}$

c)

$16v^{14}$

d)

$16v^{12}$

7.

Write the answer with a positive index $g^{-5}$

a)

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

b)

$g^5$

8.

$Simplify\ the\ following:\ 2x^{-9}\times8x^4$

a)

$16x^{-13}$

b)

$-16x^5$

c)

$6x^{-5}$

d)

$16x^{-5}$

9.

$Write\ with\ correct\ indices\ \ \ \ \left(s^5z^3\right)^{-4}\ \$

a)

$s^1z^{-1}$

b)

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

c)

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

d)

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

10.

$\frac{y^5}{y^9}$ Write with positive indices.

a)

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

b)

$y^4$

c)

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

d)

$y^5$

11.

$\frac{2a^4b^6c^{ }}{a^2b^8c^3}$ Simplify and write with positive indices

a)

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

b)

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

c)

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

d)

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

Index Laws 4-7

Total questions: 11

Worksheet time: 6mins

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