Quiz about Exponents and Radicals Practice Quiz

Question 1

Simplify: $$\frac{a^2}{a^7}$$

Accepted Answer

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

Accepted Answer

$$a^{-5}$$

Answer

$$a^5$$

Answer

$$a^9$$

Question 2

Write with positive exponents: $$\frac{1}{a^{-2}}$$

Accepted Answer

$$a^2$$

Answer

$$a^{-2}$$

Answer

$$\frac{1}{a}$$

Answer

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

Question 3

Simplify: $$\left(a^3\right)^5$$

Accepted Answer

$$a^{15}$$

Answer

$$a^8$$

Answer

$$a^{35}$$

Answer

$$a^{-2}$$

Question 4

Simplify: $$\left(3a\right)^0$$

Accepted Answer

$$1$$

Answer

$$0$$

Answer

$$3$$

Answer

$$31$$

Question 5

$$3a^0$$

Accepted Answer

$$3$$

Answer

$$0$$

Answer

$$1$$

Answer

$$31$$

Question 6

Simplify: $$a^3\cdot a^{-4}\cdot a^5$$

Accepted Answer

$$a^4$$

Answer

$$a^6$$

Answer

$$a^{-60}$$

Answer

$$a^{-7}$$

Question 7

Simplify: $$\left(\frac{2a}{4b^3}\right)^3$$

Accepted Answer

$$\frac{8a^3}{64b^9}$$

Answer

$$\frac{6a^3}{12b^9}$$

Answer

$$\frac{6a^4}{12b^6}$$

Answer

$$\frac{8a^3}{64b^6}$$

Question 8

Simplify: $$\frac{16a^{12}b^6}{4a^4b^{-3}}$$

Accepted Answer

$$4a^8b^9$$

Answer

$$4a^3b^{-2}$$

Answer

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

Answer

$$4a^8b^3$$

Question 9

Simplify: $$\left(\frac{2x}{y^4}\right)^2$$

Accepted Answer

$$\frac{4x^2}{y^8}$$

Answer

$$\frac{2x^2}{y^8}$$

Answer

$$\frac{2x^2}{y^6}$$

Answer

$$\frac{4x^2}{y^6}$$

Question 10

Simplify: $$\left(a^2b\right)^4$$

Accepted Answer

$$a^8b^4$$

Answer

$$a^6b^4$$

Answer

$$a^8b$$

Answer

$$a^2b^4$$

Question 11

Simplify: $$\frac{a^{18}}{a^{-6}}$$

Accepted Answer

$$a^{24}$$

Answer

$$a^{-3}$$

Answer

$$a^{12}$$

Answer

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

Question 12

Simplify: $$\left(2a^4b^3\right)^5$$

Accepted Answer

$$32a^{20}b^{15}$$

Answer

$$10a^{20}b^{15}$$

Answer

$$7a^{20}b^{15}$$

Answer

$$32a^9b^8$$

Question 13

Simplify: $$\frac{a^4b^8}{a^2b^4}$$

Accepted Answer

$$a^2b^4$$

Answer

$$a^2b^2$$

Answer

$$a^6b^{12}$$

Answer

$$a^{12}b^{32}$$

Question 14

Simplify: $$\frac{a^{-10}}{a^{-5}}$$

Accepted Answer

$$a^{-5}$$

Accepted Answer

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

Answer

$$a^2$$

Answer

$$\frac{1}{a^{-5}}$$

Question 15

Which is an irrational number?

Accepted Answer

$$\sqrt{8}$$

Answer

$$\sqrt{9}$$

Answer

$$\frac{\sqrt{125}}{\sqrt{5}}$$

Answer

$$\sqrt{121}$$

Question 16

What is the simplified form of $$(4\sqrt{3})^2$$ ?

Accepted Answer

48

Answer

16

Answer

12

Answer

24

Question 17

Simplify $$4(\sqrt{3})^2$$ .

Accepted Answer

$$12$$

Answer

$$16$$

Answer

$$24$$

Answer

$$48$$

Question 18

What is the result of $$\sqrt{6}·4\sqrt{6}$$ ?

Accepted Answer

$$24$$

Answer

$$48$$

Answer

$$36$$

Answer

$$12$$

Question 19

What is the result of rationalizing the denominator of $$\frac{7}{8\sqrt{8}}$$ ?

Accepted Answer

$$\frac{7\sqrt{8}}{64}$$

Accepted Answer

$$\frac{7\sqrt{2}}{32}$$

Answer

$$\frac{7\sqrt{8}}{8}$$

Answer

$$\frac{7}{64}$$

Question 20

Rationalize the denominator of $$\frac{\sqrt{2}}{\sqrt{6}}$$ .

Accepted Answer

$$\frac{\sqrt{3}}{3}$$

Answer

$$\frac{\sqrt{12}}{6}$$

Answer

$$\frac{\sqrt{6}}{3}$$

Answer

$$\frac{\sqrt{12}}{3}$$

Question 21

What is the simplified form of $$\frac{\sqrt{8}}{7}$$ ?

Accepted Answer

$$\frac{2\sqrt{2}}{7}$$

Answer

$$\frac{\sqrt{2}}{7}$$

Answer

$$\frac{4\sqrt{2}}{7}$$

Answer

$$\frac{2\sqrt{2}}{14}$$

Question 22

Rationalize the denominator of $$\frac{3\sqrt{3}}{\sqrt{12}}$$ .

Accepted Answer

$$\frac{3}{2}$$

Answer

$$\frac{3\sqrt{6}}{6}$$

Answer

$$\frac{3\sqrt{6}}{4}$$

Answer

$$\frac{3\sqrt{6}}{12}$$

Question 23

Simplify $$3\sqrt{6}-4\sqrt{6}$$ .

Accepted Answer

$$-\sqrt{6}$$

Answer

$$\sqrt{6}$$

Answer

$$-7\sqrt{6}$$

Answer

$$7\sqrt{6}$$

Question 24

What is the result of $$-3\sqrt{7}+4\sqrt{7}$$ ?

Accepted Answer

$$\sqrt{7}$$

Answer

$$-\sqrt{7}$$

Answer

$$7\sqrt{7}$$

Answer

$$-7\sqrt{7}$$

Question 25

Simplify the expression: $$3\sqrt{18}-2\sqrt{2}$$ .

Accepted Answer

$$7\sqrt{2}$$

Answer

$$5\sqrt{2}$$

Answer

$$3\sqrt{2}$$

Answer

$$4\sqrt{2}$$

Question 26

Simplify the expression: $$-3\sqrt{5}-\sqrt{6}-\sqrt{5}$$ .

Accepted Answer

$$-4\sqrt{5}-\sqrt{6}$$

Answer

$$-2\sqrt{5}-\sqrt{6}$$

Answer

$$-3\sqrt{5}-2\sqrt{6}$$

Answer

$$-4\sqrt{5}-2\sqrt{6}$$

Question 27

Simplify the expression: $$\sqrt{28x^2}$$ .

Accepted Answer

$$2x\sqrt{7}$$

Answer

$$4x\sqrt{7}$$

Answer

$$3x\sqrt{7}$$

Answer

$$5x\sqrt{7}$$

Question 28

Simplify the expression: $$\sqrt{50x^4y}$$ .

Accepted Answer

$$5x^2\sqrt{2y}$$

Answer

$$5x^2\sqrt{y}$$

Answer

$$5x\sqrt{2y}$$

Answer

$$5x\sqrt{y}$$

Question 29

Simplify the expression: $$4z\sqrt{28y^{10}z^3}$$ .

Accepted Answer

$$8y^5z^2\sqrt{7z}$$

Answer

$$8y^5z^2\sqrt{7}$$

Answer

$$28y^5z^2\sqrt{4}$$

Answer

$$8y^5z\sqrt{3}$$

Question 30

Simplify the expression: $$2x\sqrt{27x^5y^6}$$ .

Accepted Answer

$$6x^3y^3\sqrt{3x}$$

Answer

$$6x^3y^3\sqrt{x}$$

Answer

$$6x^2y^3\sqrt{3x}$$

Answer

$$6x^2y^3\sqrt{x}$$

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