ANSWER
C. 1/49
EXPLANATION
The given expression is
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } [/tex]
Recall that:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
We apply this product rule of exponents to get:
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{5}{6} + - \frac{7}{6} } [/tex]
This implies that:
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{12}{6} } [/tex]
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - 2} [/tex]
Recall again that:
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
We apply this rule to get:
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{ {7}^{2} } [/tex]
This simplifies to:
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{49} [/tex]
