Montana Math MT.PLUS.NUM.REAS.1

MathGrades 9–12Numeric Reasoning

The Standard

Extend the properties of exponents to rational exponents, including converting between exponential and radical forms.

2026 Montana Mathematics Content Standards · Number and Quantity

Teacher's field guide

What Students Need to Do: Students rewrite fractional exponents as roots and powers, and rewrite radicals using exponents. They use exponent rules to simplify expressions such as 27^(2/3).
What Mastery Looks Like: A student can write 16^(3/4) as the fourth root of 16, cubed, and get 8. They can explain why the denominator names the root and the numerator names the power.
Common Misconceptions: Students may read 16^(3/4) as (16^3)/4. Others take the fourth root but forget to cube the result. Some try to find an even root of a negative number in the real numbers.
How to Assess It: Exit ticket: Evaluate 32^(2/5) by rewriting it as a radical, then rewrite the cube root of x^2 using an exponent.

Lesson moves

Build a 3 by 3 by 3 cube with 27 snap cubes, then arrange 9 cubes into a square to model 27^(2/3).
Ask partners: Why does 27^(2/3) equal 9? Have them explain what the 3 and 2 each do.
Play exponent bingo: call out 81^(1/2), 8^(2/3), and 16^(3/4); students simplify and mark 9, 4, or 8.
Give students a cube-shaped gift box with volume 1,000 cubic centimeters; ask them to find one face's area using 1,000^(2/3).

Free download

$Preview of the MT.PLUS.NUM.REAS.1 printable worksheet$

A ready-to-print activity worksheet aligned to MT.PLUS.NUM.REAS.1, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.