Algebra 1 Unit 5: Exponents and Exponential Functions

Exponent rules, rational exponents, exponential equations and growth and decay models. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Exponent rulesNo calculator

Simplify $(2x^3)^4$.

1. $16x^{7}$
2. $2x^{12}$
3. $8x^{12}$
4. $16x^{12}$

Question 2

Exponent rulesNo calculator

Simplify $\frac{12x^5y^2}{4x^2y^6}$.

1. $\frac{3x^{7}}{y^{8}}$
2. $3x^{3}y^{4}$
3. $\frac{3x^{3}}{y^{4}}$
4. $\frac{8x^{3}}{y^{4}}$

Question 3

Rational exponentsNo calculator

Evaluate $27^{\frac{2}{3}}$.

1. $3$
2. $9$
3. $18$
4. $81$

Question 4

Negative exponentsNo calculator

Evaluate $4^{-2}+2^{-3}$.

1. $\frac{3}{16}$
2. $-24$
3. $\frac{1}{24}$
4. $\frac{3}{8}$

Question 5

Rational exponentsNo calculator

Which expression is equal to $\sqrt[3]{x^{2}}$ for $x>0$?

1. $x^{\frac{2}{3}}$
2. $x^{\frac{3}{2}}$
3. $x^{-\frac{2}{3}}$
4. $x^{6}$

Question 6

Exponential modelsNo calculator

A town of 12,000 people grows by 3% each year. Which equation gives its population $P$ after $t$ years?

1. $P=12000+0.03t$
2. $P=12000(0.97)^{t}$
3. $P=12000(1.03)^{t}$
4. $P=12000(1.3)^{t}$

Question 7

Exponential modelsCalculator

A car worth 24,000 dollars loses 15% of its value each year. What is it worth after 4 years, to the nearest dollar?

1. $12{,}528$
2. $9{,}600$
3. $12{,}528.15$
4. $14{,}400$

Question 8

Exponential modelsNo calculator

The table shows an exponential function. Which equation fits it?

x	0	1	2	3
y	5	15	45	135

1. $y=5x^{3}$
2. $y=10x+5$
3. $y=5\cdot 3^{x}$
4. $y=3\cdot 5^{x}$

Question 9

Exponential equationsNo calculator

Solve $2^{x+1}=32$.

1. $x=3$
2. $x=5$
3. $x=16$
4. $x=4$

Question 10

Exponential equationsNo calculator

Solve $9^{x}=27^{x-1}$.

1. $x=\frac{3}{5}$
2. $x=3$
3. $x=-3$
4. $x=1$

Question 11

Exponential modelsNo calculator

A 200-milligram sample of a substance loses half its mass every 5 hours. How many milligrams are left after 20 hours?

1. $12.5$
2. $50$
3. $25$
4. $100$

Question 12

Exponential modelsNo calculator

The value of a machine is modeled by $V=800(0.92)^{t}$, where $t$ is in years. Which describes the change each year?

1. 8% decrease
2. 0.92% decrease
3. 8% increase
4. 92% decrease