Solve (3/4)^4div(3/4)^920

$$( \frac { 3 } { 4 } ) ^ { 4 } \div ( \frac { 3 } { 4 } ) ^ { 9 } 20$$

Evaluate

$$\frac{20480}{243}\approx 84.279835391$$

Solution Steps

Rewrite \left(\frac{3}{4}\right)^{9} as \left(\frac{3}{4}\right)^{4}\times \left(\frac{3}{4}\right)^{5}. Cancel out \left(\frac{3}{4}\right)^{4} in both numerator and denominator.

$$\frac{1}{\left(\frac{3}{4}\right)^{5}}\times 20$$

Calculate \frac{3}{4} to the power of 5 and get \frac{243}{1024}.

$$\frac{1}{\frac{243}{1024}}\times 20$$

Divide 1 by \frac{243}{1024} by multiplying 1 by the reciprocal of \frac{243}{1024}.

$$1\times \frac{1024}{243}\times 20$$

Multiply 1 and \frac{1024}{243} to get \frac{1024}{243}.

$$\frac{1024}{243}\times 20$$

Express \frac{1024}{243}\times 20 as a single fraction.

$$\frac{1024\times 20}{243}$$

Multiply 1024 and 20 to get 20480.

$$\frac{20480}{243}$$

Factor

$$\frac{2 ^ {12} \cdot 5}{3 ^ {5}} = 84\frac{68}{243} = 84.2798353909465$$