Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Rewrite an exponential expression to reveal structure
Problem
Rewrite \(3\cdot~2^{t+4}\) in \(a\cdot~b^t\) form. Split the exponent using the product rule for powers, absorb the constant power into the coefficient, and identify the revealed \(t=0\) coefficient and growth factor.
Big Picture
What this problem is really about
A sum in an exponent becomes a product of same-base powers. We’ll separate the variable and constant exponent parts, evaluate the constant power, absorb it into the outside coefficient, and interpret the equivalent a times b to the t form through its zero-input value and unchanged interval factor.
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