Quotient Property and Zero Exponents

The quotient property and zero exponents. In MathBound, the free Algebra I adventure game, Balloon Popper 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

Quotient Property. Simplify an expression using the Quotient Property where the larger exponent is in the numerator.
Zero Exponent Property. Simplify an expression by recognizing that any non-zero base raised to the power of zero is 1.
Quotient to a Power Property. Simplify an expression by distributing an exponent to a quotient of variables.
Divide Monomials. Divide a monomial by a monomial with a single variable and integer coefficients.

Worked examples

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

Example 1 · Quotient Property

Find

the

value

of

\frac{3 ^{8}}{3 ^{7}} .

Show the worked steps

$Dividing$ $powers$ $of$ $the$ $same$ $base$ $subtracts$ $the$ $exponents.$
$\frac{3 ^{8}}{3 ^{7}} = 3 = 3 .$

Answer: $3$

Example 2 · Zero Exponent Property

Simplify:

(457)^{0}

$- 1$
$0$
$1$
$457$

Show the worked steps

$Any$ $non-zero$ $base$ $raised$ $to$ $the$ $power$ $zero$ $is$ $1.$
$That$ $holds$ $for$ $negative$ $numbers$ $too:$ $(457)^{0} = 1.$

Answer: $1$

Example 3 · Quotient to a Power Property

What

goes

in

the

box?

(\frac{a}{b ^{2}})^{□} = \frac{a ^{5}}{b ^{10}}

$6$
$10$
$5$
$3$

Show the worked steps

$The$ $exponent$ $reaches$ $the$ $numerator$ $and$ $the$ $denominator$ $alike.$
$a$ $became$ $a^{5},$ $so$ $the$ $power$ $is$ $5;$ $check:$ $b^{2}$ $to$ $the$ $5$ $is$ $b^{10} .$

Answer: $5$

Where it is in your textbook

Textbook	Lessons
Standard course	7.1
Big Ideas Math Algebra 1	6.1
Big Ideas Math Algebra 1 (2022)	6.1
CPM Core Connections Algebra	3.1.1, 3.1.2
enVision Algebra 1	6-1
enVision Algebra 1 (2024)	6-1
Glencoe Algebra 1	7-2
Holt McDougal Larson Algebra 1	7.2, 7.3
Math Nation Algebra 1 (Florida B.E.S.T.)	1.4, 2.2, 2.3, 2.9
Open Up NC Math 1 (MVP)	2.5
OpenStax Elementary Algebra 2e	6.5
Pearson Algebra 1 Common Core	7-1, 7-4
Reveal Algebra 1	8-2
SpringBoard Algebra 1	19

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