Solve [(4/3)^-2]^4div(64/27)^4/(frac{27{64})^3}

$$\frac { [ ( \frac { 4 } { 3 } ) ^ { - 2 } ] ^ { 4 } \div ( \frac { 64 } { 27 } ) ^ { 4 } } { ( \frac { 27 } { 64 } ) ^ { 3 } }$$

Evaluate

$$\frac{177147}{4194304}=0.042235136$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$\frac{\frac{\left(\frac{4}{3}\right)^{-8}}{\left(\frac{64}{27}\right)^{4}}}{\left(\frac{27}{64}\right)^{3}}$$

Calculate \frac{4}{3} to the power of -8 and get \frac{6561}{65536}.

$$\frac{\frac{\frac{6561}{65536}}{\left(\frac{64}{27}\right)^{4}}}{\left(\frac{27}{64}\right)^{3}}$$

Calculate \frac{64}{27} to the power of 4 and get \frac{16777216}{531441}.

$$\frac{\frac{\frac{6561}{65536}}{\frac{16777216}{531441}}}{\left(\frac{27}{64}\right)^{3}}$$

Divide \frac{6561}{65536} by \frac{16777216}{531441} by multiplying \frac{6561}{65536} by the reciprocal of \frac{16777216}{531441}.

$$\frac{\frac{6561}{65536}\times \frac{531441}{16777216}}{\left(\frac{27}{64}\right)^{3}}$$

Multiply \frac{6561}{65536} and \frac{531441}{16777216} to get \frac{3486784401}{1099511627776}.

$$\frac{\frac{3486784401}{1099511627776}}{\left(\frac{27}{64}\right)^{3}}$$

Calculate \frac{27}{64} to the power of 3 and get \frac{19683}{262144}.

$$\frac{\frac{3486784401}{1099511627776}}{\frac{19683}{262144}}$$

Divide \frac{3486784401}{1099511627776} by \frac{19683}{262144} by multiplying \frac{3486784401}{1099511627776} by the reciprocal of \frac{19683}{262144}.

$$\frac{3486784401}{1099511627776}\times \frac{262144}{19683}$$

Multiply \frac{3486784401}{1099511627776} and \frac{262144}{19683} to get \frac{177147}{4194304}.

$$\frac{177147}{4194304}$$

Factor

$$\frac{3 ^ {11}}{2 ^ {22}} = 0.04223513603210449$$