Problem preview

A-SSE.3.c Warmup M2-013-A10-V03

Use exponent properties to transform exponential expressions and interpret growth/decay rates.

Determine whether two exponential expressions are equivalent by rewriting with exponent rules

Problem

Determine whether \(5^t+5^{2}\) and \(5^{t+2}\) are equivalent. Simplify each expression separately, contrast addition with the product created by the exponent-sum rule, and justify the conclusion for all \(t\).

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They are not equivalent because 5t ⁺ ² = 5t · 5² = 25 · 5t, not 5t + 25.

They are equivalent because 5t ⁺ ² = 5t + 25. The product rule gives 5t · 25, not a sum.

They are equivalent because 5² = 10. In fact, 5² = 25, and exponent addition produces multiplication.

They are equivalent because both expressions include 5t and 25. One expression adds these terms while the other multiplies them.

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Curriculum context

Course: Math II
Standard: A-SSE.3.c
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Use exponent properties to transform exponential expressions and interpret growth/decay rates.
Problem type: Determine whether two exponential expressions are equivalent by rewriting with exponent rules