Question

simplify. express your answer using positive exponents.\\(\frac{f^{7}}{f^{-6}}\\)

Explanation:

Step1: Recall exponent rule for division

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

Step2: Simplify the exponent

Simplify \( 7 - (-6) \). Subtracting a negative is like adding the positive, so \( 7 + 6 = 13 \).
\( f^{7 - (-6)} = f^{13} \)

Answer:

\( f^{13} \)