Answer: C) [tex]\frac{1}{49}[/tex]
Step-by-step explanation:
[tex]7^-^\frac{5}{6}*7^-^\frac{7}{6}[/tex]
In order to make our exponents positive, we use a rule that says that if we have: [tex]a^-1=\frac{1}{a^1}[/tex]
[tex]\frac{1}{7^\frac{5}{6} }*\frac{1}{7^\frac{7}{6} }[/tex]
We have the same base 7, we only have to add the exponents.
[tex]\frac{1}{7^\frac{5}{6}^+^\frac{7}{6} }[/tex]
I'm going to solve the denominator separately so that you don't have to struggle to see the small numbers.
[tex]\frac{5}{6}+\frac{7}{6}=\frac{12}{6}=2[/tex]
The resulting fraction is:
[tex]\frac{1}{7^2} =\frac{1}{49}[/tex]
