Rational Exponents

Rational exponents. In MathBound, the free Algebra I adventure game, Sprout-Root Sid asks these problems, and the only way past is to solve them.

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

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

What you will practice

Simplify a^(1/n). Convert an expression with a unit fraction exponent to a radical and evaluate.
Simplify a^(m/n). Convert an expression with a fractional exponent to a radical and evaluate using root(n)(a)^m.
Negative Rational Exponents. Evaluate an expression with a negative rational exponent by taking the reciprocal first.
Laws of Exponents. Multiply terms with rational exponents by finding a common denominator and adding exponents.

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

Write

1 1^{\frac{1}{3}}

as

a

radical.

Show the worked steps

Answer: $311$

Simplify:

(\frac{1}{9})^{\frac{3}{2}}

Show the worked steps

Answer: $\frac{1}{27}$

Simplify:

8 1^{\frac{- 1}{2}}

Show the worked steps

$A$ $negative$ $exponent$ $means$ $the$ $reciprocal,$ $not$ $a$ $negative$ $answer.$
$8 1^{\frac{1}{2}} = 9,$ $so$ $the$ $answer$ $is$ $\frac{1}{9} .$

Answer: $\frac{1}{9}$

Textbook	Lessons
Standard course	7.3
Big Ideas Math Algebra 1	6.2
Big Ideas Math Algebra 1 (2022)	6.2
Carnegie Learning Algebra I	M3 1.2
CPM Core Connections Algebra	7.2.1
CPS Skyline Algebra	2.4-2.5, 2.6-2.7
enVision Algebra 1	6-1
enVision Algebra 1 (2024)	6-1
Eureka Math Algebra I (EngageNY)	3.8
Glencoe Algebra 1	7-3
HMH Into Algebra 1	1.2
Math Nation Algebra 1 (Florida B.E.S.T.)	1.5, 1.6, 1.7
MVP Mathematics I (Integrated Math 1)	2.4, 2.7
OpenStax Elementary Algebra 2e	9.8
Pearson Algebra 1 Common Core	7-5
Reveal Algebra 1	8-4
SpringBoard Algebra 1	19