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Mathorio

Worksheet

Product Rule for Exponents

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Show your work for each problem.

1.
Which expression is equal to $5^2 \cdot 5^6$ ?
1. a) $5^8$
2. b) $10^8$
3. c) $5^{12}$
4. d) $25^8$
2.
$2^3 \cdot 2^4 = 2^{\square}$ . What number goes in the box?
3.
Which product can be written as a single power with the product rule?
1. a) $2^3 \cdot 5^2$
2. b) $5^2 \cdot 3^3$
3. c) $7^3 \cdot 7^5$
4. d) $2^4 + 2^3$
4.
$x \cdot x^6 = x^{\square}$ . What is the exponent?
5.
Write $3^2 \cdot 3^3$ as a single power and find its value.
6.
Simplify $10^2 \cdot 10^4$ and write the result as an ordinary number.
7.
Simplify $4x^3 \cdot 2x^5$ .
1. a) $8x^{15}$
2. b) $8x^8$
3. c) $6x^8$
4. d) $8x^2$
8.
$y^4 \cdot y^2 \cdot y^3 = y^{\square}$ . What is the exponent?
9.
Sam writes $2^3 \cdot 2^4 = 4^7$ . What went wrong?
1. a)He should have multiplied the exponents
2. b)He should have subtracted the exponents
3. c)Nothing, the answer is correct
4. d)He multiplied the bases instead of keeping the base 2
10.
Simplify $3x^2 \cdot 4x^3$ , then find its value for $x = 2$ .
11.
Simplify $5a \cdot 2a^4$ .
12.
A rectangle is $2^5$ cm long and $2^3$ cm wide. Find its area in cm².
13.
$3^{\square} \cdot 3^4 = 3^{10}$ . What number goes in the box?
14.
Which product is NOT equal to $2^{10}$ ?
1. a) $2 \cdot 2^9$
2. b) $2^4 \cdot 2^6$
3. c) $2^2 \cdot 2^5$
4. d) $2^5 \cdot 2^5$
15.
Find the value of $(-2)^3 \cdot (-2)^4$ .
16.
Simplify $2a^3b \cdot 5a^4b^2$ .
17.
Write $4^3 \cdot 2^5$ as a single power of 2 and find its value.
18.
Find $n$ if $x^n \cdot x^3 \cdot x^n = x^{11}$ .