Balloon BundlerPowerhouse · exponents and exponential functions

Ties balloons in bundles of bundles: the product and power properties.

Product and Power Properties of Exponents

The product and power properties. In MathBound, the free Algebra I adventure game, Balloon Bundler asks these problems, and the only way past is to solve them.

Part of Exponents and Exponential Functions: chapter 7 of the standard course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Product Property. Simplify expressions using the Product Property of Exponents by adding exponents of the same base.
Power Property. Simplify expressions using the Power Property of Exponents by multiplying exponents.
Product to a Power Property. Simplify expressions by distributing an exponent to a product of variables.
Combine Properties. Simplify complex expressions by applying the Power Property and then the Product Property sequentially.
Multiply Monomials. Multiply two basic monomials involving one variable.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Product Property

Eli

simplified

m^{4} \cdot m^{5}

as

m^{20} .

What

is

the

correct

simplification?

$2 m^{9}$
$m^{10}$
$m^{9}$
$m^{20}$

Show the worked steps

$m^{20}$ $multiplies$ $the$ $exponents.$
$Multiplying$ $powers$ $of$ $the$ $same$ $base$ $adds$ $the$ $exponents.$
$4 + 5 = 9,$ $so$ $the$ $answer$ $is$ $m^{9} .$

Answer: $m^{9}$

Example 2 · Power Property

Simplify:

(4^{3})^{3} . Write

the

answer

as

a

power

of

4 .

$4^{9}$
$1 2^{9}$
$4^{27}$
$4^{6}$

Show the worked steps

$A$ $power$ $raised$ $to$ $a$ $power$ $multiplies$ $the$ $exponents.$
$3 \cdot 3 = 9,$ $so$ $4^{9} .$

Answer: $4^{9}$

Example 3 · Product to a Power Property

Simplify:

(a b c)^{2}

$a^{2} b^{2} c$
$a^{2} b^{2} c^{2}$
$a b c^{2}$
$a^{2} b c$

Show the worked steps

$The$ $exponent$ $reaches$ $every$ $factor$ $inside$ $the$ $brackets.$
$Raise$ $every$ $factor$ $to$ $the$ $power$ $2 : a^{2} b^{2} c^{2} .$

Answer: $a^{2} b^{2} c^{2}$

Where it is in your textbook

Textbook	Lessons
Standard course	7.1, 7.3, 7.7
Big Ideas Math Algebra 1	6.1, 6.5
Big Ideas Math Algebra 1 (2022)	6.1, 6.5
Carnegie Learning Algebra I	M3 1.2
CPM Core Connections Algebra	3.1.1, 7.2.1
CPS Skyline Algebra	2.6-2.7
enVision Algebra 1	6-1
enVision Algebra 1 (2024)	6-1
Glencoe Algebra 1	7-1
HMH Into Algebra 1	1.2, 15.1
Holt McDougal Larson Algebra 1	7.1
Math Nation Algebra 1 (Florida B.E.S.T.)	1.4, 1.6, 2.1, 2.3
MVP Mathematics I (Integrated Math 1)	2.6, 2.7
Open Up NC Math 1 (MVP)	2.5
OpenStax Elementary Algebra 2e	6.2, 9.8
Pearson Algebra 1 Common Core	7-2, 7-3
Reveal Algebra 1	8-1, 8-4, 8-7
SpringBoard Algebra 1	19

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