Quiz about radicals and laws of exponents

Question 1

Which expression represents 9 times the difference of y and 3?

Accepted Answer

9(y-3)

Answer

9 - 3y

Answer

9y - 3

Answer

9y - 3y

Question 2

What is the range of the relation shown below?

{ (-3, 1), (6, -3), (8, -3), (3, 2), (-9, 4) }

Accepted Answer

{-3, 1, 2, 4}

Answer

all real numbers

Answer

{-9, -3, 3, 6, 8}

Answer

{-9, -3, 1, 2, 3, 4, 6, 8}

Question 3

The graph of which equation has a slope of 2 and passes through the point (-1, 2)?

Accepted Answer

$$y=2x+4$$

Answer

$$y=2x+8$$

Answer

$$y=\frac{3}{4}x+2$$

Answer

$$y=\frac{4}{3}x+2$$

Question 4

At the baseball stadium, four hot dogs and three bags of candy cost $14.37. Twelve hot dogs and nine bags of candy cost $24.74. If h represents the number of hot dogs and c represents a bag of candy, what system of equations represents the situation?

Accepted Answer

$$4h+3c=14.37$$ $$12h+9c=24.74$$

Answer

$$4h+3c=24.74$$ $$12h+9c=14.37$$

Answer

$$h+c=14.37$$ $$h-c=24.74$$

Answer

You cannot write a system of equations from the information above

Question 5

Which expression is equivalent to $$a^{-4}\cdot a^6\cdot a^{-12}$$

Accepted Answer

$$\frac{1}{a^{10}}$$

Answer

$$a^{288}$$

Answer

$$a^{22}$$

Answer

$$\frac{1}{a^{120}}$$

Question 6

If $$\frac{x^y}{x^4}=x^8$$ , what is the value of y?

Accepted Answer

12

Answer

2

Answer

4

Answer

10

Question 7

Simplify $$\frac{9a^3b^5}{-3ab^2}$$

Accepted Answer

$$-3a^2b^3$$

Answer

$$3a^3b^2$$

Answer

$$-\frac{1a^2}{3b^3}$$

Answer

$$\frac{1}{a^2b^3}$$

Question 8

Which is a simplified form of the following expression using only positive exponents?

$$10x^{-4}y^3z^{-7}$$

Accepted Answer

$$\frac{10y^3}{x^4z^7}$$

Answer

$$\frac{y^3}{10x^4z^7}$$

Answer

$$\frac{1}{10x^4y^3z^7}$$

Answer

$$10xyz^{14}$$

Question 9

Simplify (-3x⁴y⁵)²

Accepted Answer

9x⁸y¹⁰

Answer

6x⁸y¹⁰

Answer

3x⁸y¹⁰

Answer

-9x⁸y¹⁰

Question 10

Simplify the expression:

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

Accepted Answer

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

Answer

$$4a^8b$$

Answer

$$a^{13}b^8$$

Answer

$$-2a^8y^7$$

Question 11

If $$\left(3x^2y^5\right)^n=9x^4y^{10}$$

Accepted Answer

2

Answer

3

Answer

5

Answer

12

Question 12

Simplify: $$\left(\frac{10m^2n^9}{2m^3n^2}\right)^0$$

Accepted Answer

1

Answer

0

Answer

$$\frac{5n^7}{m}$$

Answer

$$8mn^7$$

Question 13

Simplify: $$\sqrt[]{75}$$

Accepted Answer

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

Answer

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

Answer

$$3\ \sqrt[]{10}$$

Answer

$$3\ \ \sqrt[]{25}$$

Question 14

Simplify: $$\sqrt[]{216}$$

Accepted Answer

$$6\ \sqrt[]{6}$$

Answer

$$2\ \sqrt[]{54}$$

Answer

$$3\ \sqrt[]{24}$$

Answer

$$5\ \sqrt[]{6}$$

Question 15

Which expression is equivalent to $$\sqrt[]{2}\ \cdot\ \sqrt[]{5}$$

Accepted Answer

$$\sqrt[]{10}$$

Answer

$$\sqrt[]{7}$$

Answer

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

Answer

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

Question 16

Which of the following is equivalent to $$\left(a^x\right)^y$$

Accepted Answer

$$a^{x\cdot y}$$

Answer

$$a^{\left(x-y\right)}$$

Answer

$$a^{\left(x+y\right)}$$

Answer

$$a^x+a^y$$

Question 17

Which of the following are equivalent to $$20^{\frac{1}{2}}$$ ? Select all correct answers

Accepted Answer

$$\sqrt[]{20}$$

Accepted Answer

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

Answer

$$\sqrt[3]{20}$$

Answer

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

Question 18

If $$\sqrt[3]{36}$$ is written with an exponent as $$36^x$$ , what is the value of x?

Accepted Answer

1/3

Answer

3

Answer

1/2

Answer

2

radicals and laws of exponents

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