Solve [2^-1/3^(2-1)div5/8]^-1*(3/4)^-1

$$[ \frac { 2 ^ { - 1 } } { 3 ^ { ( 2 - 1 ) } } \div \frac { 5 } { 8 } ] ^ { - 1 } \cdot ( \frac { 3 } { 4 } ) ^ { - 1 }$$

Evaluate

$$5$$

Solution Steps

Divide \frac{2^{-1}}{3^{2-1}} by \frac{5}{8} by multiplying \frac{2^{-1}}{3^{2-1}} by the reciprocal of \frac{5}{8}.

$$\left(\frac{2^{-1}\times 8}{3^{2-1}\times 5}\right)^{-1}\times \left(\frac{3}{4}\right)^{-1}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$\left(\frac{\frac{1}{2}\times 8}{3^{2-1}\times 5}\right)^{-1}\times \left(\frac{3}{4}\right)^{-1}$$

Multiply \frac{1}{2} and 8 to get 4.

$$\left(\frac{4}{3^{2-1}\times 5}\right)^{-1}\times \left(\frac{3}{4}\right)^{-1}$$

Subtract 1 from 2 to get 1.

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

Calculate 3 to the power of 1 and get 3.

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

Multiply 3 and 5 to get 15.

$$\left(\frac{4}{15}\right)^{-1}\times \left(\frac{3}{4}\right)^{-1}$$

Calculate \frac{4}{15} to the power of -1 and get \frac{15}{4}.

$$\frac{15}{4}\times \left(\frac{3}{4}\right)^{-1}$$

Calculate \frac{3}{4} to the power of -1 and get \frac{4}{3}.

$$\frac{15}{4}\times \frac{4}{3}$$

Multiply \frac{15}{4} and \frac{4}{3} to get 5.

$$5$$

Factor

$$5$$