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An exponent tells you how many times to multiply the base by itself.
\[a^n = \underbrace{a \times a \times \cdots \times a}_{n \text{ times}}\]
The base is the repeated factor (here 2) and the exponent is the count of multiplications (here 5), giving \(2^5 = 32\).
\[2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\]
Dividing \(a^n\) by itself gives 1, and the quotient rule gives \(a^n / a^n = a^{n-n} = a^0\), so \(a^0\) must equal 1.
\[a^0 = 1 \quad (a \neq 0)\]
\(x^1\) equals \(x\) itself, because raising to the first power means a single copy of the base.
\[x^1 = x\]
A negative exponent means take the reciprocal of the corresponding positive power.
\[x^{-n} = \frac{1}{x^n} \quad (x \neq 0)\]