Question

select all the expressions that are equivalent to $\frac{10^{-2}}{10^{2}}$.$\frac{1}{10^{-1}}$$10^{4}$$\frac{1}{10^{4}}$$10^{0}$save answer

Explanation:

Step1: Apply exponent division rule

When dividing exponents with the same base, subtract the denominator exponent from the numerator exponent:
$$\frac{10^{-2}}{10^{2}} = 10^{-2-2} = 10^{-4}$$

Step2: Rewrite negative exponent

A negative exponent means the reciprocal of the positive exponent:
$$10^{-4} = \frac{1}{10^{4}}$$

Step3: Evaluate other options

• $\frac{1}{10^{-1}} = 10^1 = 10$, not equivalent
• $10^4 = 10000$, not equivalent
• $10^0 = 1$, not equivalent

Answer:

$\frac{1}{10^{4}}$