Deck 13: Exponents and Radicals

Question 1

Simplify and write without negative exponents: $2 a x^{-1}$

Answer 1

$\frac{2 a}{x}$

Question 2

Simplify and write without negative exponents: $a^{-1} z^{3}$

Answer 2

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

Question 3

Simplify and write without negative exponents: $\left(a x^{2}-b y^{2}\right)^{-2}$

Answer 3

$\frac{1}{a^{2} x^{4}-2 a b x^{2} y^{2}+b^{2} y^{4}}$

Question 4

Simplify and write without negative exponents: $4 a^{-1}-(5 b)^{-2}$

Question 5

Simplify and write without negative exponents: $6 x^{-3} y^{2}+4 x y^{-1}$

Question 6

Simplify and write without negative exponents: $\left(2 x^{2}+4 y^{2}\right)^{-2}$

Question 7

Simplify and write without negative exponents: $\left(2 x^{3} y^{4}\right)^{-3}$

Question 8

Simplify and write without negative exponents: $2 m^{-2}+\frac{n^{2}}{2}$

Question 9

Simplify and write without negative exponents: $2 x^{-2} y^{2}+\frac{2 x^{2} y^{-2}}{3}$

Question 10

Simplify and write without negative exponents: $\left(x^{n}+y^{n-1}\right)\left(x^{n-1}-y^{n-2}\right)$

Question 11

Simplify and write without negative exponents: $\left(x^{a}-n-y^{a+n}\right)\left(x^{a+n}-2 y^{a-n}\right)$

Question 12

Simplify and write without negative exponents: $\left(\frac{1}{x^{2}}\right)^{-n}$

Question 13

Simplify and write without negative exponents: $\left(\frac{q}{2 z}\right)^{-2}$

Question 14

Simplify and write without negative exponents: $\left(\frac{4 x}{8 y}\right)^{-1}$

Question 15

Simplify and write without negative exponents: $\left(\frac{15 x^{2}}{9 x y z}\right)^{-2}$

Question 16

Simplify and write without negative exponents: $\left(\frac{2 x}{42 x^{2}}\right)^{-4 m}$

Question 17

Simplify and write without negative exponents: $\left(\frac{2 x y z^{2}}{4 x^{2} y}\right)^{-2}$

Question 18

Simplify and write without negative exponents: $\left(\frac{3 x^{-2}}{5 y^{-4}}\right)^{3}$

Question 19

Simplify and write without negative exponents: $\left(\frac{3 x^{2} y z^{2}}{9 x y^{2} z^{3}}\right)^{-2}$

Question 20

Simplify and write without negative exponents: $\left(\frac{x y^{n+1}}{x^{n-1} y}\right)^{-3}$

Question 21

Simplify and write without negative exponents: $\left(\frac{4 a^{2} b^{3}}{3 b c^{4}}\right)^{-2}$

Question 22

Simplify and write without negative exponents: $\left(\frac{4 x^{-2} y^{4}}{3 a^{3} b^{-4}}\right)^{-3}$

Question 23

Simplify and write without negative exponents: $\frac{x^{a^{2}}-\left(y^{a}\right)^{a}}{\left(x^{2 a}\right)^{a}-y^{2 a^{2}}}$

Question 24

Simplify and write without negative exponents: $\left(\frac{4 x^{5}}{7 a^{2} y^{n}} \div \frac{x^{n+3}}{y^{n+m}}\right) \frac{a^{m}}{y^{n+3}}$

Question 25

Simplify and write without negative exponents: $\left(\frac{a^{n+1}}{a^{n^{2}+1}}\right) \div\left(\frac{a^{n-1}}{a^{n+1}}\right)^{n}$

Question 26

Simplify and write without negative exponents: $\frac{x^{3} y^{4}-3 x^{2} y^{4}+2 x y^{5}}{x y^{3}-y^{4}}$

Question 27

Simplify and write without negative exponents: $\frac{2 x^{3} y^{4}-4 x^{2} y^{5}+8 x^{4} y^{3}}{2 x^{2} y^{2}}$

Question 28

Simplify and write without negative exponents: $\frac{9 x^{2} y^{2}+12 x^{5}+18 x^{4} y^{3}}{3 x^{2} y^{2}}$

Question 29

When current $I$ causes a power $P$ in a resistance $R$ , the resistance is given by $R=\frac{P}{I^{2}}$ . Write an expression without fractions for the resistance when the current is doubled.

Question 30

The volume of a cylinder with radius $r$ and perpendicular height $h$ is given by $V=\pi r^{2} h$ . If the radius is reduced by $20 \%$ , write a simplified expression for the volume.

Question 31

Simplify: $\sqrt[5]{7776}$

Question 32

Simplify: $\frac{\sqrt[3]{64}}{\sqrt[4]{256}}$

Question 33

Simplify: $\sqrt[4]{\frac{625}{2401}}$

Question 34

Express in radical form: $\frac{a^{\frac{-1}{2}}}{b}$

Question 35

Express in radical form: $(4 a)^{\frac{-1}{4}}$

Question 36

Express in radical form: $x^{\frac{1}{2}} y^{\frac{-1}{2}}$

Question 37

Express in radical form: $3 a^{\frac{-1}{2}}(a-b)^{\frac{3}{8}}$

Question 38

Express in radical form: $4 a^{\frac{-2}{3}}(a+b)^{\frac{-1}{2}}$

Question 39

Express in exponential form: $\sqrt[3]{x^{3}-y^{3}}$

Question 40

Express $3 \sqrt{a^{2} b^{3} c}$ in exponential form.

Question 41

Express $5 \sqrt[5]{32 x^{2} y^{3} z^{-1}}$ in exponential form.

Question 42

Express $\sqrt[3]{\frac{a^{3}-b^{3}}{a^{-1} b^{2}}}$ in exponential form.

Question 43

Express $\sqrt{\frac{a^{3} b^{-1}}{a^{2}-b^{2}}}$ in exponential form.

Question 44

Write in simplest form: $\sqrt{496}$

Question 45

Write in simplest form: $\sqrt{12}$

Question 46

Write in simplest form: $\sqrt[4]{32}$

Question 47

Write in simplest form: $\sqrt{x^{2} y^{4} z^{6}}$

Question 48

Write in simplest form: $2 \sqrt{72 x^{3} y^{4}}$

Question 49

Write in simplest form: $\sqrt{4 a^{2}+8 a b+4 b^{2}}$

Question 50

Write in simplest form: $a \sqrt{3 a^{2}-12 a+12}$

Question 51

Write in simplest form: $y \sqrt{x^{2} y-2 x y^{2}+y^{3}}$

Question 52

Simplify and write without negative exponents: $\frac{x^{\frac{2}{3}}-y^{\frac{2}{3}}}{x^{\frac{1}{3}}-y^{\frac{1}{3}}}$

Question 53

Simplify and write without negative exponents: $\frac{x-y}{x^{0.5}-y^{0.5}}$

Question 54

Write in simplest form: $3 \sqrt{\frac{9}{16}}$

Question 55

Write in simplest form: $15 \sqrt{\frac{16}{625}}$

Question 56

Write in simplest form: $3 \sqrt{\frac{4 a^{2}}{9 b^{4}}}$

Question 57

Write in simplest form: $\sqrt{\frac{5 a^{2} b^{3}}{8 x}}$

Question 58

Write in simplest form: $(a+b) \sqrt{\frac{a-b}{a c+b c}}$

Question 59

Write the expression in its simplest form: $\sqrt{a^{2}-\frac{2 a^{2}}{3}}$

Question 60

The one of the two shorter sides in a right triangle is 2 times longer than the other. Use the Pythagorean theorem to write an expression for the hypotenuse, and simplify.

Question 61

Combine $\sqrt{50}-\sqrt{8}$ . Leave your answer in radical form.

Question 62

Combine $\sqrt{112}+\sqrt{252}-\sqrt{175}$ . Leave your answer in radical form.

Question 63

Combine $\sqrt[3]{864}+\sqrt[3]{108}+\sqrt[3]{500}$ . Leave your answer in radical form.

Question 64

Combine $\sqrt{45}-\frac{1}{2} \sqrt{80}+3 \sqrt{20}$ . Leave your answer in radical form.

Question 65

Combine $\sqrt{\frac{4}{9}}-\sqrt{\frac{25}{2}}+2 \sqrt{\frac{9}{2}}$ . Leave your answer in radical form.

Question 66

Combine $\sqrt{12 x^{4}}-\sqrt{27 x^{4}}+\sqrt{75 x^{4}}$ . Leave your answer in radical form.

Question 67

Combine $2 a \sqrt{9 a b^{2} c}-5 b \sqrt{4 a^{3} c}+\sqrt{16 a^{3} b^{2} c}$ . Leave your answer in radical form.

Question 68

Combine $a \sqrt[3]{54 a^{3} b^{4}}+b \sqrt[3]{16 a^{6} b}$ . Leave your answer in radical form.

Question 69

Multiply $2 \sqrt{6 a^{3} b}$ by $\sqrt{8 b}$ .

Question 70

Multiply $4 \sqrt{2}$ by $2 \sqrt{4}$ .

Question 71

Multiply $4 \sqrt[3]{3}$ by $3 \sqrt{2}$ .

Question 72

Multiply $\sqrt{\frac{2 a}{3 b}}$ by $\sqrt{\frac{6 a}{4 c}}$ .

Question 73

Multiply $\sqrt{3 x}$ by $(\sqrt{6 y}-\sqrt{12 x})$ .

Question 74

Multiply $\sqrt[3]{2 x^{2}}$ by $(\sqrt[3]{x}-\sqrt[3]{4})$ .

Question 75

Multiply $(3 \sqrt{x}-y)$ by $(4 \sqrt{x}+y)$ .

Question 76

Multiply $(4 \sqrt{x y}-2 y)$ by $(2 \sqrt{x y}+x)$ .

Question 77

Multiply $(3 \sqrt{x}-2 \sqrt{2})$ by $(\sqrt{x}+4 \sqrt{2 y})$ .

Question 78

Multiply $(5+2 \sqrt{-7})$ by $(6-5 \sqrt{-7})$ .

Question 79

Multiply $(\sqrt{a}-\sqrt{-b})$ by $(\sqrt{a}+3 \sqrt{-b})$ .

Question 80

Multiply $\left(\sqrt{x}+2 \sqrt{y^{3}}\right)$ by $\left(\sqrt{y}+4 \sqrt{x^{3}}\right)$ .