Question

evaluate. write your answer as a whole number or as a simplified fraction. 7⁻⁶ · 7⁵ =

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$
$7^{-6} \cdot 7^{5} = 7^{-6+5}$

Step2: Simplify the exponent

Calculate the sum of the exponents
$7^{-6+5} = 7^{-1}$

Step3: Rewrite negative exponent as fraction

A negative exponent means reciprocal: $a^{-k} = \frac{1}{a^k}$
$7^{-1} = \frac{1}{7}$

Answer:

$\frac{1}{7}$