Use exponent properties to transform exponential expressions and interpret growth/decay rates.
Rewrite an exponential expression with a new base using the power-of-a-power rule
Problem
Rewrite \(5(4)^t\) with base \(2\). State the power relationship between \(4\) and \(2\), apply \((b^k)^t=b^{kt}\), and explain why the coefficient \(5\) does not change.
Big Picture
What this problem is really about
To change the exponential base, first express the old base as an exact power of the requested one. We’ll substitute that power, multiply the nested exponents with the power-of-a-power rule, leave the separate coefficient untouched, and check the equivalent forms at a simple input.
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