Solve ((frac{3/5)^{5}(3/4)^-2}{(3/4)^-1(3/4)^6})^-2=

$$( \frac { ( \frac { 3 } { 5 } ) ^ { 5 } ( \frac { 3 } { 4 } ) ^ { - 2 } } { ( \frac { 3 } { 4 } ) ^ { - 1 } ( \frac { 3 } { 4 } ) ^ { 6 } } ) ^ { - 2 } =$$

Evaluate

$$\frac{791015625}{268435456}=2.946762834$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and 6 to get 5.

$$\left(\frac{\left(\frac{3}{5}\right)^{5}\times \left(\frac{3}{4}\right)^{-2}}{\left(\frac{3}{4}\right)^{5}}\right)^{-2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{\left(\frac{3}{5}\right)^{5}}{\left(\frac{3}{4}\right)^{7}}\right)^{-2}$$

Calculate \frac{3}{5} to the power of 5 and get \frac{243}{3125}.

$$\left(\frac{\frac{243}{3125}}{\left(\frac{3}{4}\right)^{7}}\right)^{-2}$$

Calculate \frac{3}{4} to the power of 7 and get \frac{2187}{16384}.

$$\left(\frac{\frac{243}{3125}}{\frac{2187}{16384}}\right)^{-2}$$

Divide \frac{243}{3125} by \frac{2187}{16384} by multiplying \frac{243}{3125} by the reciprocal of \frac{2187}{16384}.

$$\left(\frac{243}{3125}\times \frac{16384}{2187}\right)^{-2}$$

Multiply \frac{243}{3125} and \frac{16384}{2187} to get \frac{16384}{28125}.

$$\left(\frac{16384}{28125}\right)^{-2}$$

Calculate \frac{16384}{28125} to the power of -2 and get \frac{791015625}{268435456}.

$$\frac{791015625}{268435456}$$

Factor

$$\frac{3 ^ {4} \cdot 5 ^ {10}}{2 ^ {28}} = 2\frac{254144713}{268435456} = 2.9467628337442875$$