Power of a Power

Name:

Class:

Date:

Show your work for each problem.

1.
Simplify $(x^3)^4$ .
1. a) $x^{7}$
2. b) $x^{81}$
3. c) $x^{12}$
4. d) $4x^{3}$
2.
$(2^3)^2 = 2^{\square}$ . What number goes in the box?
3.
Simplify $(a^5)^2$ by writing it as a product first.
4.
Evaluate $(3^2)^2$ .
5.
Which expression is equal to $(5y)^2$ ?
1. a) $25y^2$
2. b) $25y$
3. c) $10y^2$
4. d) $5y^2$
6.
Compare $(2^2)^3$ and $(2^3)^2$ .
7.
$(2x^3)^4 = \square \, x^{12}$ . What number goes in the box?
8.
What is the value of $2^{3^2}$ (without brackets)?
1. a)512
2. b)128
3. c)36
4. d)64
9.
Simplify $(3x^2)^3$ .
10.
Simplify $\left(\frac{x^2}{3}\right)^3$ .
11.
$(10^2)^3 \cdot 10^4 = 10^{\square}$ . What number goes in the box?
12.
Which statement is true for all numbers $a$ and $b$ ?
1. a) $(2a)^3 = 2a^3$
2. b) $(a + b)^2 = a^2 + b^2$
3. c) $(ab)^2 = a^2 b^2$
4. d) $(a^2)^3 = a^5$
13.
Show with numbers that $(3 + 4)^2 \neq 3^2 + 4^2$ .
14.
Simplify $\frac{(x^4)^3 \cdot x^2}{(x^3)^4}$ .
15.
$(2a^2b^3)^4 = 16a^8 b^{\square}$ . What number goes in the box?
16.
Simplify $(2x^2y)^3 \cdot (xy^2)^2$ .
17.
Simplify $\left(\frac{2x^3}{y^2}\right)^3$ .
1. a) $\frac{6x^9}{y^6}$
2. b) $\frac{2x^9}{y^6}$
3. c) $\frac{8x^6}{y^5}$
4. d) $\frac{8x^9}{y^6}$
18.
A cube has edges of length $3 \cdot 10^2$ cm, so its volume is $(3 \cdot 10^2)^3$ cm³. Find the volume.