Negative Exponents

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Show your work for each problem.

1.
What is the value of $2^{-3}$ ?
1. a) $-8$
2. b) $\frac{1}{8}$
3. c) $-6$
4. d) $8$
2.
Which expression is equal to $\frac{1}{5^2}$ ?
1. a) $5^{-2}$
2. b) $5^{2}$
3. c) $\frac{1}{5^{-2}}$
4. d) $-5^{2}$
3.
Write $10^{-2}$ as a decimal.
4.
Evaluate $4^{-1}$ . Write the answer as a fraction.
5.
Which expression is equal to $\frac{x^{-3}}{y^{-2}}$ ?
1. a) $\frac{y^2}{x^3}$
2. b) $\frac{x^3}{y^2}$
3. c) $-\frac{y^2}{x^3}$
4. d) $x^{3}y^{2}$
6.
Evaluate $3^{-2}$ . Write the answer as a fraction.
7.
Write $0.001$ as a power of 10. What is the exponent?
8.
Which number is the largest?
1. a) $10^{-2}$
2. b) $10^{-1}$
3. c) $2^{-1}$
4. d) $2^{-3}$
9.
Evaluate $\left(\frac{2}{5}\right)^{-2}$ . Write the answer as a fraction.
10.
Evaluate $\frac{1}{2^{-4}}$ .
11.
Evaluate $\left(\frac{3}{4}\right)^{-3}$ . Write the answer as a fraction.
12.
Simplify $x^{-5} \cdot x^{2}$ and write it as $\frac{1}{x^{\square}}$ . What goes in the box?
13.
Simplify $\frac{4a^{-3}b^{2}}{2a^{2}b^{-1}}$ and write it with positive exponents.
1. a) $\frac{2b}{a}$
2. b) $2a^{5}b^{3}$
3. c) $\frac{b^{3}}{2a^{5}}$
4. d) $\frac{2b^{3}}{a^{5}}$
14.
Evaluate $2x^{-3}$ for $x = 2$ . Write the answer as a fraction.
15.
Evaluate $2^{-2} + 2^{-3}$ . Write the answer as a fraction.
16.
Simplify $\frac{(x^{-2})^{3}}{x^{-10}}$ to a single power $x^{\square}$ . What is the exponent?
17.
Evaluate $\frac{2^{-3} \cdot 2^{5}}{2^{-1}}$ .
18.
Multiply $(4 \times 10^{-3}) \times (2 \times 10^{5})$ and write the result as an ordinary number.