Same base? Work the powers. Same power, different base? Merge bases: $5^2\times3^2=15^2$, $7^4\div5^4=(\tfrac{7}{5})^4$. Reflex: Add power, minus power, times power — matching powers let you merge the bases.

Zero power vanishes to 1; negative power flips into a reciprocal; fractional power's bottom is the root, top is the power. Reflex: Flip negative powers; bottom's the root — $8^{\frac{2}{3}} = (\sqrt[3]{8})^2$.

Tidy each side to one power per base, then match powers base-by-base — two bases give two equations to solve simultaneously.

Reflex: Tidy first, compare after — a bare $b$ means $b^1$, not nothing.

Peel the constant off the exponent so every term shows a bare $3^n$ — then $3^n$ is a common factor: take it out and cancel. Reflex: Split, factorize, cancel — then press the calculator.

Asked for $10^x$, not $x$? Don't solve for $x$ — treat $10^x$ as one block. Reflex: Split into prime bases, solve, then glue $2^x \cdot 5^x$ back into $10^x$.

Same base, compare powers. If terms like $4^x$ and $2^x$ block one base per side, substitute instead. Reflex: One power double the other? Sub $u = a^x$ and solve the quadratic.

Same shape for $2^x$, $10^x$, $e^x$ — growth rate keeps increasing. Reflex: Recall x-axis is asymptote; curve always passes through $(0,1)$.

Start from $e^x$: minus in front flips in the $x$-axis; minus in front of $x$ flips in the $y$-axis; both together flip twice. Every curve gets closer and closer to the $x$-axis — never touching it. Reflex: Learn the shape — know which axis each flip hits.

Draw $ke^{\pm x}$ first, then shift by $c$ ($+c$ up, $-c$ down). Asymptote moves from $y=0$ to $y=c$ — the curve gets closer and closer to it, but never touches. Reflex: Resub $x=0$ into the FULL equation for the new $y$-intercept, and check $y=0$ (often no solution).