Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
The last six problems use exponents and radicals in contexts: file sizes, garden fences, half-life, falling objects and a ladder. Give exact answers first, then decimals.
Standards: N-RN.A.1, N-RN.A.2 · Level: Grade 9 Algebra 1
Problem 2 Quotient of powers ★★★
Simplify x9x4.
Problem 3 Power of a power ★★★
Simplify (x2)6.
Problem 4 Negative exponent ★★★
Write 3−2 as a fraction.
Problem 5 Between two integers ★★★
Between which two consecutive integers does √20 lie? Use the number line.
Problem 6 Multiply monomials ★★★
Simplify (3x2y3)(4x5y).
Problem 7 Divide monomials ★★★
Simplify 18a7b26a3b5 using positive exponents.
Problem 8 Power of a product ★★★
Simplify (2x3)4 and (−3x2)3.
Problem 9 Positive exponents only ★★★
Rewrite x−3y2z−4 with only positive exponents.
Problem 10 Rational exponent evaluation ★★★
Evaluate 82/3 and 163/4.
Problem 11 Radical and exponent forms ★★★
Rewrite in the other form. (a) ∛(x5) (b) √x (c) y3/2.
Problem 12 Simplify a square root ★★★
Simplify √72.
Problem 13 Square side length ★★★
A square has area 48 square inches. Find its side length in simplest radical form and to the nearest hundredth.
Problem 14 Radical with a variable ★★★
Simplify √(18x6) for x ≥ 0.
Problem 15 Rectangle with radical sides ★★★
A rectangle has width √8 feet and length √18 feet. Find its exact area and exact perimeter.
Problem 16 File sizes ★★★
A file of 213 bytes is copied 27 times. How many bytes in total, written as a power of 2 and as a number? Then divide the total evenly among 25 drives.
Problem 17 Square garden fence ★★★
A square garden has area 200 square feet. Find its side length and the length of fence needed around it, in simplest radical form and to the nearest hundredth.
Problem 18 Half-life ★★★
A sample’s mass in grams is A = 64(1/2)t/6 after t days. Find the mass at t = 18 and at t = 9 in exact form, and approximate the second.
Problem 19 Falling object ★★★
The time in seconds for an object to fall d feet is t = √(d/16). Find t for a 72-foot drop in simplest radical form and to the nearest hundredth, and for a 100-foot drop.
Problem 20 Ladder against a wall ★★★
A ladder rests against a wall. Its base is 6 feet from the wall and it reaches 12 feet up the wall. Find the length of the ladder in simplest radical form and to the nearest hundredth.
