Free Printable Exponents and radicals

1.

Simplify the next expression: $-4xy\left(-2x^4y\right)$

a)

$-6x^4y$

b)

$6x^4y$

c)

$8x^5y^2$

d)

$-8x^4y^2$

2.

Simplify the next expression: $2y^5\cdot3y^{-2}\cdot4y^{-1}$

a)

$9y^2$

b)

$9y^{10}$

c)

$24y^2$

d)

$24y^{10}$

3.

Simplify the next expression: $\frac{4a^3b^2}{3a^3b^{-4}}$

a)

$\frac{4}{3}b^2$

b)

$\frac{4}{3b^2}$

c)

$\frac{4}{3}ab^2$

d)

$\frac{4}{3}b^6$

4.

Simplify the next expression: $\left(\frac{7a^3b^3c}{14a^5b^3c}\right)^{^2}$

a)

$\frac{14bc}{28a^2}$

b)

$\frac{14a^2bc}{28}$

c)

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

d)

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

5.

Simplify the next expression: $-\frac{12}{3}m^{-2}n^3$

a)

$-4\frac{n^3}{m^2}$

b)

$4\frac{n^3}{m^2}$

c)

$4m^2n^3$

d)

$-4m^2n^3$

6.

Simplify the next expression: $w^{\frac{3}{4}}\cdot w^{\frac{1}{8}}$

a)

$w^{\frac{4}{8}}$

b)

$w^{\frac{7}{8}}$

c)

$w^{\frac{4}{12}}$

d)

$w^{\frac{3}{24}}$

7.

Reexpress in radical form: $a^{\frac{3}{5}}$

a)

$\sqrt[3]{a^5}$

b)

$\sqrt[5]{a^3}$

8.

Reexpress in exponential form: $\sqrt[4]{a^3}$

a)

$a^{\frac{3}{4}}$

b)

$a^{\frac{4}{3}}$

9.

Simplify the next radical: $2\sqrt[]{90}$

a)

$10\sqrt[]{5}$

b)

$10\sqrt[]{6}$

c)

$6\sqrt[]{10}$

d)

$2\sqrt[]{30}$

10.

Simplify the next radical: $\sqrt[]{\frac{64}{100}}$

a)

$\frac{2}{3}$

b)

$\frac{3}{4}$

c)

$\frac{4}{5}$

d)

$\frac{8}{10}$

11.

Simplify the next radical: $4\sqrt[3]{16x^6y^4z^3}$

a)

$16x^3y^2z\sqrt[]{z}$

b)

$8x^2yz\sqrt[]{2y}$

c)

$8x^2yz\sqrt[3]{2y}$

d)

$4x^2yz\sqrt[3]{16y}$

12.

Simplify the next radical expression: $4a\sqrt[]{72a^5b^7}$

a)

$12a^3b^3\sqrt[]{8ab}$

b)

$16a^3b^3\sqrt[]{18ab}$

c)

$24a^3b^3\sqrt[]{2ab}$

13.

Simplify the next expression: $\left(27m^4n^9\right)^{\frac{1}{3}}$

a)

$3mn^3$

b)

$3mn^3\sqrt[3]{m}$

c)

$9mn^3$

d)

$9mn^3\sqrt[3]{m}$

14.

Multiply and determine the simplest expression: $\left(a-3\right)\left(b-7\right)$

a)

$ab+21$

b)

$-3a-7b$

c)

$-3a-7b+21$

d)

$ab-7a-3b+21$

15.

Multiply and determine the simplest expression: $5x^3\left(3x^5+5x^2-4\right)$

a)

$8x^8+10x^5-9x^3$

b)

$8x^{15}+10x^6-9$

c)

$15x^8+25x^5-20x^3$

d)

$15x^{15}+25x^6-20$

16.

Determine the simplest expression: $\left(\frac{ab^3}{a^2b^2c^2}\right)^{^0}$

a)

$0$

b)

$1$

c)

$abc^2$

d)

$\frac{b}{ac^2}$

17.

Simplify the next radical expression: $\frac{\sqrt[]{9n^6}}{\sqrt[]{36m^8}}$

a)

$\frac{3n^3}{6m^4}$

b)

$\frac{n^3}{3m^4}$

c)

$\frac{n^3}{2m^4}$

d)

$\frac{n^3}{4m^4}$

18.

Determine the simplest expression for: $2a+\frac{3}{5}-\frac{2}{6}-a$

a)

$a+\frac{4}{15}$

b)

$a+\frac{1}{11}$

c)

$a-\frac{6}{30}$

d)

$a+\frac{8}{30}$

19.

Multiply and determine the simplest expression: $\left(\sqrt[]{5n}-2\right)\left(-3\sqrt[]{5n}-5\right)$

a)

$-3\sqrt[]{5n}+10$

b)

$-10\sqrt[]{5n}+10$

c)

$-3n\sqrt[]{5n}+\sqrt[]{5n}+10$

d)

$-15n+\sqrt[]{5n}+10$

20.

Multiply and determine the simplest radical expression: $\left(-4n\sqrt[]{6n^3}\right)\left(-4\sqrt[]{18n^2}\right)$

a)

$-16n\sqrt[]{108n^6}$

b)

$24n^2\sqrt[]{3n}$

c)

$-24n^4\sqrt[]{3}$

d)

$96n^2\sqrt[]{3n}$

21.

Determine the simplest expression: $5a\sqrt[3]{3a}+2\sqrt[3]{3a^4}-\sqrt[3]{3a}$

a)

$7a\sqrt[3]{3a}-\sqrt[3]{3a}$

b)

$5a\sqrt[]{3a}+2a^2\sqrt[]{3a}-\sqrt[]{3a}$

c)

$5a\sqrt[3]{3a}+2a\sqrt[3]{3a}-\sqrt[3]{3a}$

d)

$5a\sqrt[]{3a}+2a^2\sqrt[]{3}-\sqrt[]{3a}$

22.

Simplify the next radical expression: $6\sqrt[]{24}-3\sqrt[]{24}$

a)

$3\sqrt[]{24}$

b)

$6\sqrt[]{12}$

c)

$6\sqrt[]{6}$

d)

$9\sqrt[]{2}$

Exponents and radicals

Total questions: 22

Worksheet time: 11mins

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