Simplify 6^(-5/4)*6^(-8/7)

$6^{- \frac{5}{4}} \cdot 6^{- \frac{8}{7}}$

Multiply $6^{- \frac{5}{4}}$ by $6^{- \frac{8}{7}}$ by adding the exponents.

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

$6^{- \frac{5}{4} - \frac{8}{7}}$

To write $- \frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$6^{- \frac{5}{4} \cdot \frac{7}{7} - \frac{8}{7}}$

To write $- \frac{8}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$6^{- \frac{5}{4} \cdot \frac{7}{7} - \frac{8}{7} \cdot \frac{4}{4}}$

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{4}$ by $\frac{7}{7}$ .

$6^{- \frac{5 \cdot 7}{4 \cdot 7} - \frac{8}{7} \cdot \frac{4}{4}}$

Multiply $4$ by $7$ .

$6^{- \frac{5 \cdot 7}{28} - \frac{8}{7} \cdot \frac{4}{4}}$

Multiply $\frac{8}{7}$ by $\frac{4}{4}$ .

$6^{- \frac{5 \cdot 7}{28} - \frac{8 \cdot 4}{7 \cdot 4}}$

Multiply $7$ by $4$ .

$6^{- \frac{5 \cdot 7}{28} - \frac{8 \cdot 4}{28}}$

Combine the numerators over the common denominator.

$6^{\frac{- 5 \cdot 7 - 8 \cdot 4}{28}}$

Simplify the numerator.

Multiply $- 5$ by $7$ .

$6^{\frac{- 35 - 8 \cdot 4}{28}}$

Multiply $- 8$ by $4$ .

$6^{\frac{- 35 - 32}{28}}$

Subtract $32$ from $- 35$ .

$6^{\frac{- 67}{28}}$

Move the negative in front of the fraction.

$6^{- \frac{67}{28}}$

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

$\frac{1}{6^{\frac{67}{28}}}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6^{\frac{67}{28}}}$

Decimal Form:

$0.01374026 \dots$