Exam Strategy

Readiness Check

You are ready when you can:

• Simplify $b^m b^n$, $(b^m)^n$, $b^{-n}$, and $b^{1/k}$ without a calculator.
• Rewrite $f(x)=a\cdot b^{x+k}$ and $f(x)=a\cdot b^{cx}$ into equivalent $ab^x$ forms.
• Explain one graphical consequence of each property.

On the AP Exam

• MCQ: pick the equivalent expression; identify which transformation matches a rewrite.
• FRQ: show equivalence steps; justify base change; connect to context (preview 2.5).
• Skills: 1.B equivalent forms; 3.A describe features after rewriting.

Tactics

1. Factor to a common base first ($4^x=(2^2)^x=2^{2x}$). 2. For $b^{x+k}$, pull out $b^k$ as a vertical multiplier. 3. For $b^{cx}$, rewrite base as $b^c$ before comparing growth. 4. Negative exponents: move to denominator immediately. 5. Roots: $b^{1/k}=\sqrt[k]{b}$; combine with power property.

Common Traps

• Illegal exponent addition with mismatched bases.
• Confusing shift $b^{x+k}$ with power $(b^x)^k$.
• Forgetting that $b^{cx}=(b^c)^x$ requires $b>0$ for standard reals.

Quick Checklist

• [ ] Common base identified
• [ ] Correct rule applied (product / power / negative / root)
• [ ] Equivalent $ab^x$ form if asked
• [ ] Graph transformation named if asked