Question

evaluate. write your answer as a whole number or as a simplified fraction.
\\(\frac{10^{-3}}{7^{-2}} = \\)
submit

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\). So we can rewrite the numerator and denominator using this rule.
For the numerator \(10^{-3}\), by the rule, it becomes \(\frac{1}{10^{3}}=\frac{1}{1000}\).
For the denominator \(7^{-2}\), by the rule, it becomes \(\frac{1}{7^{2}}=\frac{1}{49}\).

Step2: Rewrite the fraction

Now our fraction \(\frac{10^{-3}}{7^{-2}}\) becomes \(\frac{\frac{1}{1000}}{\frac{1}{49}}\). When dividing by a fraction, we multiply by its reciprocal. So \(\frac{\frac{1}{1000}}{\frac{1}{49}}=\frac{1}{1000}\times\frac{49}{1}\).

Step3: Multiply the fractions

Multiplying the numerators and denominators, we get \(\frac{1\times49}{1000\times1}=\frac{49}{1000}\).

Answer:

\(\frac{49}{1000}\)