Problem preview

A-SSE.3.c Warmup M2-013-A10-V04

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

Compare \(4^{2x}\) with \(16^x\) by rewriting \(16\) in base \(4\). Multiply the nested exponents and state whether the expressions are equal for every \(x\).

Answer choices

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They are not equivalent because 4²ˣ has base 4 while 16ˣ has base 16. Rewriting 16 as 4² shows the expressions match.

They are not equivalent because 16ˣ = 4ˣ ⁺ ². Since 16 = 4², 16ˣ = 4²ˣ.

They are equivalent because 4²ˣ = (4²)ˣ = 16ˣ.

They are not equivalent because 4²ˣ = 8x. Exponentiation does not convert to multiplication by x.

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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