Question

rewrite using a single positive exponent.\\(\frac{7^{-2}}{7^{-6}}\\)

Explanation:

Step1: Apply exponent rule for division

When dividing exponents with the same base, we subtract the exponents: \( \frac{a^m}{a^n} = a^{m - n} \). Here, \( a = 7 \), \( m = -2 \), and \( n = -6 \). So we calculate \( -2 - (-6) \).

Step2: Simplify the exponent

\( -2 - (-6) = -2 + 6 = 4 \). So \( \frac{7^{-2}}{7^{-6}} = 7^{4} \).

Answer:

\( 7^{4} \)