Question

select the correct answer.
simplify the following expression.
$7^{-\frac{5}{6}} \cdot 7^{-\frac{7}{6}}$
a. $\frac{1}{49}$
b. $\frac{1}{14}$
c. $49$
d. $14$

Explanation:

Step1: Add exponents (same base)

When multiplying terms with the same base, add exponents: $7^{-\frac{5}{6} + (-\frac{7}{6})}$

Step2: Calculate exponent sum

$$-\frac{5}{6} - \frac{7}{6} = \frac{-5 -7}{6} = \frac{-12}{6} = -2$$
So the expression becomes $7^{-2}$

Step3: Rewrite negative exponent

A negative exponent means reciprocal: $7^{-2} = \frac{1}{7^2}$

Step4: Compute denominator

$7^2 = 49$, so $\frac{1}{7^2} = \frac{1}{49}$

Answer:

A. $\frac{1}{49}$