Free Printable Radical & Rational Exponents Practice

1.

Tell whether the following question is TRUE or FALSE. $\left(4x^3y^4\right)^2=16x^6y^8$

a)

TRUE

b)

FALSE

2.

When simplified $\left(-3x^2\right)^2\left(4x^3\right)$ equals to

a)

$-36x^{12}$

b)

$36x^7$

c)

$-36x^7$

d)

$36x^{12}$

3.

Simplify the expression $\frac{3x^7y^6}{x^3y^8}=\frac{3x^?}{y^?}$ . What are the needed power for $x$ and $y$ ?

a)

21 and 48

b)

4 and 2

c)

10 and 14

d)

2 and 2

4.

Simplify the expression $\frac{2x^{-2}y^{-2}}{16x^{-12}y^2}=$ . What are the needed power for $x$ and $y$ ?

a)

$-24x^{14}$

b)

$\frac{4}{x^2}$

c)

$\frac{x^{10}}{8y^4}$

d)

$\frac{1}{16x^8y^4}$

5.

Which expression is equivalent to $\frac{18c^8d^9}{9c^3d^6}$ ?

a)

$9c^{11}d^{15}$

b)

$2c^5d^3$

c)

$9c^5d^3$

d)

$2c^{11}d^{15}$

6.

Which expression is equivalent to $\left(x^9yz^4\right)^5$

a)

$x^{14}y^6z^9$

b)

$x^{14}y^5z^9$

c)

$x^{45}yz^{20}$

d)

$x^{45}y^5z^{20}$

7.

a⁰ = ?

a)

1

b)

2

c)

3

d)

0

8.

$\frac{x^8}{x^5}$

a)

$x^{13}$

b)

$x^3$

c)

$\frac{x^5}{x^8}$

d)

$x^{40}$

9.

$\frac{x^8}{x^5}$

a)

$x^{13}$

b)

$x^3$

c)

$\frac{x^5}{x^8}$

d)

$x^{40}$

10.

$y^4\ \circ\ y^6$

(a)

11.

$\left(x^2\right)^4$

(a)

12.

$a^{-4}$

a)

$a^4$

b)

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

c)

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

d)

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

13.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

14.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

15.

Simplify:
(3t²)³

a)

9t⁶

b)

9t⁵

c)

27t⁶

d)

27t⁵

16.

Rewrite the expression as a rational exponent

Reescribe la expresión como un exponente racional.

$\sqrt[3]{5^2}$

a)

$2^{\frac{5}{3}}$

b)

$3^{\frac{2}{5}}$

c)

$5^{\frac{2}{3}}$

d)

$5^{\frac{3}{2}}$

17.

Rewrite the expression in radical form

Reescribe la expresión en forma radical.

$8^{\frac{1}{3}}$

a)

$\sqrt[3]{8}$

b)

$\sqrt[1]{3^8}$

c)

$\sqrt[3]{1^8}$

d)

$\sqrt[8]{3}$

18.

Rewrite the expression in radical form

Reescribe la expresión en forma radical.

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

a)

$\sqrt[2]{4^3}$

b)

$\sqrt[3]{4^2}$

c)

$\sqrt[4]{3^2}$

d)

$\sqrt[4]{2^3}$

19.

Simplify the following expression

Simplifica la siguiente expresión

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

a)

$x^6y^6$

b)

$\frac{y^6}{x^5}$

c)

$\frac{x^6}{y^6}$

d)

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

20.

Rewrite the following

∛x⁵

a)

x^3/5

b)

x^5/3

c)

x²

d)

x³⋅x⁵

21.

Write in exponential form
∜(3x)³

a)

3x³⁄ ⁴

b)

(3x)³∕ ⁴

c)

(3x)⁴⁄ ³

d)

3x⁴⁄ ³

22.

Which expression with a fractional exponent best represents √7 ?

a)

7^½

b)

7¼

c)

7⅓

d)

2⁷

23.

∜m³ is the same as which answer?

a)

m^3/4

b)

m¹²

c)

m^4/3

d)

m⁷

24.

Simplify the expression $(\sqrt{a})^4$ using rational exponents.

a)

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

b)

$a^{2}$

c)

$a^{\frac{4}{2}}$

d)

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

25.

Express the radical $\sqrt[4]{y^3}$ as a rational exponent.

a)

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

b)

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

c)

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

d)

$y^{4}$

26.

Convert the radical expression $\sqrt[5]{z^2}$ to a rational exponent.

a)

$z^{\frac{2}{5}}$

b)

$z^{\frac{5}{2}}$

c)

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

d)

$z^{2}$

27.

Rewrite in exponential form.

$\left(\sqrt{7b}\right)^3$

a)

$\left(7b\right)^{\frac{3}{1}}$

b)

$7b^{\frac{3}{2}}$

c)

$\left(7b\right)^{\frac{1}{2}}$

d)

$\left(7b\right)^{\frac{3}{2}}$

28.

Rewrite in exponential form.

$\ ^{\ ^3\sqrt{v}}$

a)

$v^{-\frac{1}{3}}$

b)

$v^{\frac{1}{3}}$

c)

$\frac{1}{v^3}$

d)

$v^{\frac{3}{1}}$

29.

Rewrite in exponential form.

$\sqrt{3r}$

a)

$3r^{\frac{1}{2}}$

b)

$\left(3r\right)^{\frac{2}{1}}$

c)

$r^{\frac{3}{2}}$

d)

$\left(3r\right)^{\frac{1}{2}}$

30.

Rewrite in exponential form.

$\left(\ ^4\sqrt{10v}\right)^5$

a)

$10v^{\frac{5}{4}}$

b)

$\left(10v\right)^{\frac{4}{5}}$

c)

$10v^{\frac{4}{5}}$

d)

$\left(10v\right)^{\frac{5}{4}}$

Radical & Rational Exponents Practice

Total questions: 30

Worksheet time: 2hrs 30mins

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