Solve 3^3/2:(2/3)^4=2/7

$$\frac { 3 ^ { 3 } } { 2 } : ( \frac { 2 } { 3 } ) ^ { 4 } = \frac { 2 } { 7 }$$

Verify

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{\frac{27}{2}}{\left(\frac{2}{3}\right)^{4}}=\frac{2}{7}$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{\frac{27}{2}}{\frac{16}{81}}=\frac{2}{7}$$

Divide \frac{27}{2} by \frac{16}{81} by multiplying \frac{27}{2} by the reciprocal of \frac{16}{81}.

$$\frac{27}{2}\times \frac{81}{16}=\frac{2}{7}$$

Multiply \frac{27}{2} times \frac{81}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 81}{2\times 16}=\frac{2}{7}$$

Do the multiplications in the fraction \frac{27\times 81}{2\times 16}.

$$\frac{2187}{32}=\frac{2}{7}$$

Least common multiple of 32 and 7 is 224. Convert \frac{2187}{32} and \frac{2}{7} to fractions with denominator 224.

$$\frac{15309}{224}=\frac{64}{224}$$

Compare \frac{15309}{224} and \frac{64}{224}.

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