Question

evaluate. write your answer as a whole number or as a simplified fraction.\\(\frac{6^{-4}}{6^{-7}} = \square\\)

Explanation:

Step1: Apply exponent quotient rule

When dividing exponents with the same base, subtract the denominator exponent from the numerator exponent: $\frac{a^m}{a^n}=a^{m-n}$
$\frac{6^{-4}}{6^{-7}}=6^{-4-(-7)}$

Step2: Simplify the exponent

Calculate the value of the new exponent:
$6^{-4+7}=6^{3}$

Step3: Compute the final value

Calculate the power of 6:
$6^3=6\times6\times6$

Answer:

216