Unit 2 · Exponents & Scientific Notation

Integer Exponent Properties

a^m · a^n = a^(m+n), (a^m)^n = a^(mn), a^0 = 1 (a ≠ 0), a^(−n) = 1/a^n.

Grade 8 State Test

NY-8.EE.1

Notes

The product rule adds exponents only when the bases match. (2³)(2⁵) = 2⁸, but (2³)(5³) = 10³ — that is a different rule (power of a product).

The number of times a base is used as a factor.

Example: In 5⁴, 5 is the base and 4 is the exponent.

Try the prompt first. The steps stay folded until you ask to see them.

Simplify (3²)⁴ · 3^(−3).

Watch for

Multiplying exponents in a product of like bases

Product of powers adds; power of a power multiplies.

Fix: Say the rule out loud before writing.

Submit each answer to check it. The key is not shown until you do.

Question 1 of 3Grade 8 State TestNY-8.EE.1Grade 8 Mathematics · Spring 2022 · Q35Non-calculatorproficient

Which expression is equivalent to 4⁻⁵ × 4⁸?

4⁻² / 4⁻¹(4³)⁻¹4² / 4⁻¹(4⁻¹)³

Choose or type an answer first. The key stays hidden until you do.

Question 2 of 3Grade 8 State TestNY-8.EE.1Grade 8 Mathematics · Spring 2023 · Q15Non-calculatorproficient

Which expression has a value of 1/16?

(4)⁻¹(4)⁻²(8)⁻²(−8)⁻²

Choose or type an answer first. The key stays hidden until you do.

Question 3 of 3Algebra I RegentsAI-N.RN.1Algebra I Regents · June 2024 · Q3Non-calculatoremerging

Which equation is always true?

x² · x³ = x⁵3x · 3² = 9²ˣ2z² = z²7ᵃ · 7ᵇ = 7ᵃᵇ

Choose or type an answer first. The key stays hidden until you do.

Rewrite every negative exponent as a reciprocal before combining.

Simplify mixed expressions with negative and zero exponents.

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