Question

question
which expression is equivalent to \\(\frac{5^{-1}}{5^{-2}}\\)?
answer
\\(\frac{1}{5^3}\\) \\(5^3\\)
\\(5\\) \\(\frac{1}{5^2}\\)

Explanation:

Step1: Apply exponent division rule

When dividing exponents with the same base, subtract the denominator exponent from the numerator exponent: $a^m \div a^n = a^{m-n}$
$\frac{5^{-1}}{5^{-2}} = 5^{-1 - (-2)}$

Step2: Simplify the exponent

Calculate the value of the exponent:
$5^{-1 + 2} = 5^{1}$

Step3: Evaluate the final term

$5^{1} = 5$

Answer:

5