Evaluate 10^-2.

Step-by-step solution

1. 1

   Apply the negative-exponent definition. A negative exponent signals a reciprocal, never a negative result:

   $a^{-n}=\frac{1}{a^{n}}\qquad\Longrightarrow\qquad10^{-2}=\frac{1}{10^{2}}$

   The commonest misreading is treating $10^{-2}$ as $-100$ or $-20$. The base stays positive; only its position moves, from numerator to denominator.

2. 2

   Evaluate the positive power.

   $10^{2}=10\times10=100$

3. 3

   Write the fraction and the decimal.

   $10^{-2}=\frac{1}{100}=0.01$

   The exponent $-2$ moves the decimal point two places left from $1$, which is the fast way to read any power of ten.

4. 4

   Check against the pattern of powers of ten. Reading downward, each step divides by $10$:

   $10^{2}=100,\quad10^{1}=10,\quad10^{0}=1,\quad10^{-1}=0.1,\quad10^{-2}=0.01$

   The sequence continues smoothly through zero and into negatives ✓, which is exactly the reason negative exponents are defined this way.

5. 5

   Confirm with the exponent laws. Multiplying by the positive power should return $1$:

   $10^{-2}\times10^{2}=10^{-2+2}=10^{0}=1$

   and indeed $0.01\times100=1$ ✓. In scientific notation $10^{-2}$ is the multiplier for centi, which is why $1$ cm $=10^{-2}$ m.