Exponent laws and powers of 10

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Learn it Same base: multiply → add exponents ($a^m \times a^n = a^{m+n}$); divide → subtract ($a^m \div a^n = a^{m-n}$); power of a power → multiply ($(a^m)^n = a^{mn}$).

Example: Simplify $\frac{3^5 \times 3^2}{3^4}$.

Numerator: $3^{5+2} = 3^7$.
Divide: $3^{7-4} = 3^3$.
$3^3 = 27$.

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