Simplify -(729/64)^(5/6)

$- {(\frac{729}{64})}^{\frac{5}{6}}$

Apply the product rule to $\frac{729}{64}$ .

$- \frac{729^{\frac{5}{6}}}{64^{\frac{5}{6}}}$

Simplify the numerator.

Rewrite $729$ as $3^{6}$ .

$- \frac{{(3^{6})}^{\frac{5}{6}}}{64^{\frac{5}{6}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{3^{6 (\frac{5}{6})}}{64^{\frac{5}{6}}}$

Cancel the common factor of $6$ .

Cancel the common factor.

$- \frac{3^{6 (\frac{5}{6})}}{64^{\frac{5}{6}}}$

Rewrite the expression.

$- \frac{3^{5}}{64^{\frac{5}{6}}}$

Raise $3$ to the power of $5$ .

$- \frac{243}{64^{\frac{5}{6}}}$

Simplify the denominator.

Rewrite $64$ as $2^{6}$ .

$- \frac{243}{{(2^{6})}^{\frac{5}{6}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{243}{2^{6 (\frac{5}{6})}}$

Cancel the common factor of $6$ .

Cancel the common factor.

$- \frac{243}{2^{6 (\frac{5}{6})}}$

Rewrite the expression.

$- \frac{243}{2^{5}}$

Raise $2$ to the power of $5$ .

$- \frac{243}{32}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{243}{32}$

Decimal Form:

$- 7.59375$

Mixed Number Form:

$- 7 \frac{19}{32}$