Solve 1/6*3/12*18/20*(a/b)^-2

$$\frac { 1 } { 6 } \times \frac { 3 } { 12 } \times \frac { 18 } { 20 } \times ( \frac { a } { b } ) ^ { - 2 }$$

Evaluate

$$\frac{3\times \left(\frac{b}{a}\right)^{2}}{80}$$

Solution Steps

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{6}\times \frac{1}{4}\times \frac{18}{20}\times \left(\frac{a}{b}\right)^{-2}$$

Multiply \frac{1}{6} and \frac{1}{4} to get \frac{1}{24}.

$$\frac{1}{24}\times \frac{18}{20}\times \left(\frac{a}{b}\right)^{-2}$$

Reduce the fraction \frac{18}{20} to lowest terms by extracting and canceling out 2.

$$\frac{1}{24}\times \frac{9}{10}\times \left(\frac{a}{b}\right)^{-2}$$

Multiply \frac{1}{24} and \frac{9}{10} to get \frac{3}{80}.

$$\frac{3}{80}\times \left(\frac{a}{b}\right)^{-2}$$

To raise \frac{a}{b} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{3}{80}\times \frac{a^{-2}}{b^{-2}}$$

Multiply \frac{3}{80} times \frac{a^{-2}}{b^{-2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3a^{-2}}{80b^{-2}}$$

Expand

$$\frac{3\times \left(\frac{b}{a}\right)^{2}}{80}$$

Solution Steps

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{6}\times \frac{1}{4}\times \frac{18}{20}\times \left(\frac{a}{b}\right)^{-2}$$

Multiply \frac{1}{6} and \frac{1}{4} to get \frac{1}{24}.

$$\frac{1}{24}\times \frac{18}{20}\times \left(\frac{a}{b}\right)^{-2}$$

Reduce the fraction \frac{18}{20} to lowest terms by extracting and canceling out 2.

$$\frac{1}{24}\times \frac{9}{10}\times \left(\frac{a}{b}\right)^{-2}$$

Multiply \frac{1}{24} and \frac{9}{10} to get \frac{3}{80}.

$$\frac{3}{80}\times \left(\frac{a}{b}\right)^{-2}$$

To raise \frac{a}{b} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{3}{80}\times \frac{a^{-2}}{b^{-2}}$$

Multiply \frac{3}{80} times \frac{a^{-2}}{b^{-2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3a^{-2}}{80b^{-2}}$$