Use exponent properties to transform exponential expressions and interpret growth/decay rates.
Evaluate using exponent properties
Problem
Evaluate \(2^{3}\cdot~2^{5}\) by first identifying the common base and applying the product rule for exponents. Show the exponent calculation, compute the exact value, and check it against \(8\cdot~32\).
Big Picture
What this problem is really about
The outermost operation is multiplication of powers with the same base, so the product rule adds their exponents. We’ll identify the common base, combine the exponent counts before evaluating, compute the single power, and check it by multiplying the values of the original factors.
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