Solve {left(frac{-1/4right)}^4*{left(3/4right)}^3}{{left(-1/4right)}^6*{left(3/4right)}^2}

$$\frac{ { \left( \frac{ -1 }{ 4 } \right) }^{ 4 } \times { \left( \frac{ 3 }{ 4 } \right) }^{ 3 } }{ { \left( \frac{ -1 }{ 4 } \right) }^{ 6 } \times { \left( \frac{ 3 }{ 4 } \right) }^{ 2 } }$$

Evaluate

$$12$$

Solution Steps

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{\left(-\frac{1}{4}\right)^{4}\times \left(\frac{3}{4}\right)^{3}}{\left(\frac{-1}{4}\right)^{6}\times \left(\frac{3}{4}\right)^{2}}$$

Calculate -\frac{1}{4} to the power of 4 and get \frac{1}{256}.

$$\frac{\frac{1}{256}\times \left(\frac{3}{4}\right)^{3}}{\left(\frac{-1}{4}\right)^{6}\times \left(\frac{3}{4}\right)^{2}}$$

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

$$\frac{\frac{1}{256}\times \frac{27}{64}}{\left(\frac{-1}{4}\right)^{6}\times \left(\frac{3}{4}\right)^{2}}$$

Multiply \frac{1}{256} and \frac{27}{64} to get \frac{27}{16384}.

$$\frac{\frac{27}{16384}}{\left(\frac{-1}{4}\right)^{6}\times \left(\frac{3}{4}\right)^{2}}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{\frac{27}{16384}}{\left(-\frac{1}{4}\right)^{6}\times \left(\frac{3}{4}\right)^{2}}$$

Calculate -\frac{1}{4} to the power of 6 and get \frac{1}{4096}.

$$\frac{\frac{27}{16384}}{\frac{1}{4096}\times \left(\frac{3}{4}\right)^{2}}$$

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

$$\frac{\frac{27}{16384}}{\frac{1}{4096}\times \frac{9}{16}}$$

Multiply \frac{1}{4096} and \frac{9}{16} to get \frac{9}{65536}.

$$\frac{\frac{27}{16384}}{\frac{9}{65536}}$$

Divide \frac{27}{16384} by \frac{9}{65536} by multiplying \frac{27}{16384} by the reciprocal of \frac{9}{65536}.

$$\frac{27}{16384}\times \frac{65536}{9}$$

Multiply \frac{27}{16384} and \frac{65536}{9} to get 12.

$$12$$

Factor

$$2^{2}\times 3$$