Simplify 7^(-5/6)*7^(-7/6)

$7^{- \frac{5}{6}} \cdot 7^{- \frac{7}{6}}$

Multiply $7^{- \frac{5}{6}}$ by $7^{- \frac{7}{6}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7^{- \frac{5}{6} - \frac{7}{6}}$

Combine the numerators over the common denominator.

$7^{\frac{- 5 - 7}{6}}$

Subtract $7$ from $- 5$ .

$7^{\frac{- 12}{6}}$

Divide $- 12$ by $6$ .

$7^{- 2}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{7^{2}}$

Raise $7$ to the power of $2$ .

$\frac{1}{49}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{49}$

Decimal Form:

$0.02040816 \dots$