Evaluate ((3/4)^6)÷((3/4)^-3)

${(\frac{3}{4})}^{6} \div {(\frac{3}{4})}^{- 3}$

Rewrite the division as a fraction.

$\frac{{(\frac{3}{4})}^{6}}{{(\frac{3}{4})}^{- 3}}$

Move ${(\frac{3}{4})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{3}{4})}^{6} {(\frac{3}{4})}^{3}$

Multiply ${(\frac{3}{4})}^{6}$ by ${(\frac{3}{4})}^{3}$ by adding the exponents.

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

${(\frac{3}{4})}^{6 + 3}$

Add $6$ and $3$ .

${(\frac{3}{4})}^{9}$

Apply the product rule to $\frac{3}{4}$ .

$\frac{3^{9}}{4^{9}}$

Raise $3$ to the power of $9$ .

$\frac{19683}{4^{9}}$

Raise $4$ to the power of $9$ .

$\frac{19683}{262144}$

The result can be shown in multiple forms.

Exact Form:

$\frac{19683}{262144}$

Decimal Form:

$0.07508468 \dots$