Exponent Mastery Worksheet
Grade 7 Math Unit Review • Part 1
Exponent Mastery Worksheet
Name:
Date: Period:
Core Exponent Properties Reference
Product \(a^m \cdot a^n = a^{m+n}\)
Quotient \(\frac{a^m}{a^n} = a^{m-n}\)
Power of Power \((a^m)^n = a^{m \cdot n}\)
Zero Power \(a^0 = 1 \; (a \neq 0)\)
Negative Exp \(a^{-n} = \frac{1}{a^n}\)
1 Applying Properties with Integer & Fractional Bases
Simplify to a single power or simplified fraction.
- \(7^{-6} \cdot 7^9\) Product Rule
Work:
Answer:
- \(\left(\frac{2}{5}\right)^3 \cdot \left(\frac{2}{5}\right)^{-5}\) Fractional Base
Work:
Answer:
- \(\left(4^{-2}\right)^3 \cdot 4^0\) Power & Zero Rule
Work:
Answer:
- \(\left(\frac{3}{4}\right)^{-2}\) Negative Exp
Work:
Value:
2 Quotient Property with Negative Integers
Be mindful of subtracting negative exponents: \(m - (-n) = m + n\)
- \(\frac{10^{-4}}{10^3}\) \(10^{(-4) - (3)}\)
Work:
Answer:
- \(\frac{x^5}{x^{-4}}\) \(x^{5 - (-4)}\)
Work:
Answer:
- \(\frac{8^{-3}}{8^{-7}}\) \(8^{(-3) - (-7)}\)
Work:
Answer:
- \(\frac{\left(\frac{1}{3}\right)^{-5}}{\left(\frac{1}{3}\right)^{-2}}\) Fractional Base
Work:
Answer:
3 Finding Missing Exponents
Determine the integer value of the missing exponent that makes the equation true.
\(5^8 \cdot 5^{\Box} = 5^3\)
\(8 + \Box = 3\)
\(\Box = \)
\(\frac{k^{-3}}{k^{\Box}} = k^4\)
\(-3 - \Box = 4\)
\(\Box = \)
\(\left(2^{\Box}\right)^{-4} = 2^{20}\)
\(\Box \cdot (-4) = 20\)
\(\Box = \)
Proficiency Target: Apply single/combined properties & solve for single missing exponent. Page 1 of 2
Grade 7 Math Unit Review • Part 2
Generating Equivalent Expressions
Write three different expressions for each target, then explain in words.
For each target power, create three different expressions that have the exact same value. Use multiplication for Expression A, division for Expression B, and a power raised to another power for Expression C.
1 Target Value: \(4^{-6}\)
Base: 4
Expression A (Multiplication)
Expression B (Division)
Expression C (Power of Power)
Explain in words why all three equal \(4^{-6}\):
2 Target Value: \(\left(\frac{2}{3}\right)^{-4}\)
Fractional Base: \(\frac{2}{3}\)
Expression A (Multiplication)
Expression B (Division)
Expression C (Power of Power)
Explain in words why all three equal \(\left(\frac{2}{3}\right)^{-4}\):
3 Target Value: \(10^{-5}\)
Base: 10
Expression A (Multiplication)
Expression B (Division)
Expression C (Power of Power)
Explain in words why all three equal \(10^{-5}\):
Equivalence Challenge: Show multiple ways to represent the same power. Page 2 of 2
