Solve (3/4)^-4:(3/4)^3*(0,75)^9

$$( \frac { 3 } { 4 } ) ^ { - 4 } : ( \frac { 3 } { 4 } ) ^ { 3 } \cdot ( 0,75 ) ^ { 9 }$$

Evaluate

$$0,5625$$

Solution Steps

Rewrite \left(\frac{3}{4}\right)^{3} as \left(\frac{3}{4}\right)^{-4}\times \left(\frac{3}{4}\right)^{7}. Cancel out \left(\frac{3}{4}\right)^{-4} in both numerator and denominator.

$$\frac{1}{\left(\frac{3}{4}\right)^{7}}\times 0,75^{9}$$

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

$$\frac{1}{\frac{2187}{16384}}\times 0,75^{9}$$

Divide 1 by \frac{2187}{16384} by multiplying 1 by the reciprocal of \frac{2187}{16384}.

$$1\times \frac{16384}{2187}\times 0,75^{9}$$

Multiply 1 and \frac{16384}{2187} to get \frac{16384}{2187}.

$$\frac{16384}{2187}\times 0,75^{9}$$

Calculate 0,75 to the power of 9 and get 0,075084686279296875.

$$\frac{16384}{2187}\times 0,075084686279296875$$

Multiply \frac{16384}{2187} and 0,075084686279296875 to get \frac{9}{16}.

$$\frac{9}{16}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {4}} = 0.5625$$