Solve {left(1-frac{1/4right)}^-3{left(4/3right)}^2}{{left(1/1^-3+3^-1right)}^4}

$$\frac{ { \left(1- \frac{ 1 }{ 4 } \right) }^{ -3 } { \left( \frac{ 4 }{ 3 } \right) }^{ 2 } }{ { \left( \frac{ 1 }{ { 1 }^{ -3 } } + { 3 }^{ -1 } \right) }^{ 4 } }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from 1 to get 4.

$$\frac{\left(1-\frac{1}{4}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}{\left(1^{4}+3^{-1}\right)^{4}}$$

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$\frac{\left(\frac{3}{4}\right)^{-3}\times \left(\frac{4}{3}\right)^{2}}{\left(1^{4}+3^{-1}\right)^{4}}$$

Calculate \frac{3}{4} to the power of -3 and get \frac{64}{27}.

$$\frac{\frac{64}{27}\times \left(\frac{4}{3}\right)^{2}}{\left(1^{4}+3^{-1}\right)^{4}}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{\frac{64}{27}\times \frac{16}{9}}{\left(1^{4}+3^{-1}\right)^{4}}$$

Multiply \frac{64}{27} and \frac{16}{9} to get \frac{1024}{243}.

$$\frac{\frac{1024}{243}}{\left(1^{4}+3^{-1}\right)^{4}}$$

Calculate 1 to the power of 4 and get 1.

$$\frac{\frac{1024}{243}}{\left(1+3^{-1}\right)^{4}}$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{\frac{1024}{243}}{\left(1+\frac{1}{3}\right)^{4}}$$

Add 1 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{\frac{1024}{243}}{\left(\frac{4}{3}\right)^{4}}$$

Calculate \frac{4}{3} to the power of 4 and get \frac{256}{81}.

$$\frac{\frac{1024}{243}}{\frac{256}{81}}$$

Divide \frac{1024}{243} by \frac{256}{81} by multiplying \frac{1024}{243} by the reciprocal of \frac{256}{81}.

$$\frac{1024}{243}\times \frac{81}{256}$$

Multiply \frac{1024}{243} and \frac{81}{256} to get \frac{4}{3}.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$