Powers and exponent laws
Multiplying powers of the same base adds the exponents, dividing subtracts them, and a power of a power multiplies them.
A worked example
Simplify 7⁵ ÷ 7² by subtracting exponents: 7³ = 343. And (5³)² = 5⁶, because the exponents multiply.
The mistake people actually make
An exponent counts repeated multiplication, so 5³ means 125, not 15. Any non-zero base raised to the power zero equals 1.