Solve [(1/5+1/8)^2:(1/5-1/8)^2*frac{90}{100}]^0*(frac{16}{3}:frac{4}{3})

$$[ ( \frac { 1 } { 5 } + \frac { 1 } { 8 } ) ^ { 2 } : ( \frac { 1 } { 5 } - \frac { 1 } { 8 } ) ^ { 2 } \cdot \frac { 90 } { 100 } ] ^ { 0 } \cdot ( \frac { 16 } { 3 } : \frac { 4 } { 3 } )$$

Evaluate

$$4$$

Solution Steps

Add \frac{1}{5} and \frac{1}{8} to get \frac{13}{40}.

$$\left(\frac{\left(\frac{13}{40}\right)^{2}}{\left(\frac{1}{5}-\frac{1}{8}\right)^{2}}\times \frac{90}{100}\right)^{0}\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Calculate \frac{13}{40} to the power of 2 and get \frac{169}{1600}.

$$\left(\frac{\frac{169}{1600}}{\left(\frac{1}{5}-\frac{1}{8}\right)^{2}}\times \frac{90}{100}\right)^{0}\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Subtract \frac{1}{8} from \frac{1}{5} to get \frac{3}{40}.

$$\left(\frac{\frac{169}{1600}}{\left(\frac{3}{40}\right)^{2}}\times \frac{90}{100}\right)^{0}\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Calculate \frac{3}{40} to the power of 2 and get \frac{9}{1600}.

$$\left(\frac{\frac{169}{1600}}{\frac{9}{1600}}\times \frac{90}{100}\right)^{0}\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Divide \frac{169}{1600} by \frac{9}{1600} by multiplying \frac{169}{1600} by the reciprocal of \frac{9}{1600}.

$$\left(\frac{169}{1600}\times \frac{1600}{9}\times \frac{90}{100}\right)^{0}\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Multiply \frac{169}{1600} and \frac{1600}{9} to get \frac{169}{9}.

$$\left(\frac{169}{9}\times \frac{90}{100}\right)^{0}\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Reduce the fraction \frac{90}{100} to lowest terms by extracting and canceling out 10.

$$\left(\frac{169}{9}\times \frac{9}{10}\right)^{0}\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Multiply \frac{169}{9} and \frac{9}{10} to get \frac{169}{10}.

$$\left(\frac{169}{10}\right)^{0}\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Calculate \frac{169}{10} to the power of 0 and get 1.

$$1\times \frac{\frac{16}{3}}{\frac{4}{3}}$$

Divide \frac{16}{3} by \frac{4}{3} by multiplying \frac{16}{3} by the reciprocal of \frac{4}{3}.

$$1\times \frac{16}{3}\times \frac{3}{4}$$

Multiply \frac{16}{3} and \frac{3}{4} to get 4.

$$1\times 4$$

Multiply 1 and 4 to get 4.

$$4$$

Factor

$$2^{2}$$