Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Work in order. Name the rule before each step, rewrite negative exponents as fractions, and put every final answer in simplest form.
Standards: 8.EE.A.1 · Level: Grade 8
Problem 1 Repeated multiplication ★★★
Write each power as repeated multiplication, then evaluate: (a) 43 (b) (−2)5 (c) 104
Problem 2 Zero and negative exponents ★★★
Evaluate: (a) 70 (b) 2−4 (c) 10−3
Problem 3 Product rule ★★★
Write each product as one power: (a) 65 · 62 (b) m9 · m4
Problem 4 Quotient rule ★★★
Write 6562 as one power, using the picture to explain what cancels.
Problem 5 Power of a power ★★★
Simplify using the picture: (23)2. Then simplify (n5)2.
Problem 6 Counting factors ★★★
The row shows 34 · 32. Write it as one power and find its value.
Problem 7 Negative exponents as fractions ★★★
Rewrite without a negative exponent and simplify: (a) 4−3 (b) (15)−2
Problem 8 Mixed exponents, one base ★★★
Evaluate: (a) 5−2 · 54 (b) 73 · 7−5
Problem 9 Power of a product ★★★
Simplify: (a) (5y)3 (b) (4m2)3 (c) (2a3)2
Problem 10 Power then divide ★★★
Evaluate (52)3 ÷ 54.
Problem 11 Fractions to a power ★★★
Evaluate: (a) (23)3 (b) (34)−2
Problem 12 Positive exponents only ★★★
Rewrite with positive exponents: (a) x−3 (b) 5a−2 (c) 1y−4
Problem 13 Complete the pattern ★★★
Fill in the three missing values in the table of powers of 5 and describe the pattern.
Problem 14 Find the error ★★★
Zoe wrote 43 · 42 = 165. Explain her mistake and give the correct result as a power and as a number.
Problem 15 Share chain ★★★
A school announcement is texted to 3 students in round 1. In each later round, every student who just received it texts 3 new students. After 6 rounds, 36 students have received it in round 6. How many students received it in round 6, and how many times as many as in round 4?
Problem 16 Nested powers ★★★
Evaluate (2−3 · 28)2 ÷ 27.
Problem 17 Simplify with two variables ★★★
Simplify and write with positive exponents: (x−2y3)−2.
Problem 18 Compare three values ★★★
Order from least to greatest: 2−3, (−2)−3, −23. Explain each value.
Problem 19 Cookie batches ★★★
A baker uses 2−3 cup of oats per cookie and bakes 26 cookies for the county fair. How many cups of oats does the baker use? Write the answer as a power of 2 and as a number.
Problem 20 Missing exponents ★★★
Find each missing exponent: (a) 7n · 7−4 = 79 (b) (5m)3 = 518 (c) 3k ÷ 3−2 = 37
