Solve (frac{3/9)^{4}(3/9)^{6}(9/3)^-2}{(3/9)^10(frac{9}{3})^4(frac{3}{9})^2}

$$\frac { ( \frac { 3 } { 9 } ) ^ { 4 } ( \frac { 3 } { 9 } ) ^ { 6 } ( \frac { 9 } { 3 } ) ^ { - 2 } } { ( \frac { 3 } { 9 } ) ^ { 10 } ( \frac { 9 } { 3 } ) ^ { 4 } ( \frac { 3 } { 9 } ) ^ { 2 } }$$

Evaluate

$$\frac{1}{81}\approx 0.012345679$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{\left(\frac{3}{9}\right)^{10}\times \left(\frac{9}{3}\right)^{-2}}{\left(\frac{3}{9}\right)^{10}\times \left(\frac{9}{3}\right)^{4}\times \left(\frac{3}{9}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 10 and 2 to get 12.

$$\frac{\left(\frac{3}{9}\right)^{10}\times \left(\frac{9}{3}\right)^{-2}}{\left(\frac{3}{9}\right)^{12}\times \left(\frac{9}{3}\right)^{4}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\left(\frac{1}{3}\right)^{10}\times \left(\frac{9}{3}\right)^{-2}}{\left(\frac{3}{9}\right)^{12}\times \left(\frac{9}{3}\right)^{4}}$$

Calculate \frac{1}{3} to the power of 10 and get \frac{1}{59049}.

$$\frac{\frac{1}{59049}\times \left(\frac{9}{3}\right)^{-2}}{\left(\frac{3}{9}\right)^{12}\times \left(\frac{9}{3}\right)^{4}}$$

Divide 9 by 3 to get 3.

$$\frac{\frac{1}{59049}\times 3^{-2}}{\left(\frac{3}{9}\right)^{12}\times \left(\frac{9}{3}\right)^{4}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{59049}\times \frac{1}{9}}{\left(\frac{3}{9}\right)^{12}\times \left(\frac{9}{3}\right)^{4}}$$

Multiply \frac{1}{59049} and \frac{1}{9} to get \frac{1}{531441}.

$$\frac{\frac{1}{531441}}{\left(\frac{3}{9}\right)^{12}\times \left(\frac{9}{3}\right)^{4}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{531441}}{\left(\frac{1}{3}\right)^{12}\times \left(\frac{9}{3}\right)^{4}}$$

Calculate \frac{1}{3} to the power of 12 and get \frac{1}{531441}.

$$\frac{\frac{1}{531441}}{\frac{1}{531441}\times \left(\frac{9}{3}\right)^{4}}$$

Divide 9 by 3 to get 3.

$$\frac{\frac{1}{531441}}{\frac{1}{531441}\times 3^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{1}{531441}}{\frac{1}{531441}\times 81}$$

Multiply \frac{1}{531441} and 81 to get \frac{1}{6561}.

$$\frac{\frac{1}{531441}}{\frac{1}{6561}}$$

Divide \frac{1}{531441} by \frac{1}{6561} by multiplying \frac{1}{531441} by the reciprocal of \frac{1}{6561}.

$$\frac{1}{531441}\times 6561$$

Multiply \frac{1}{531441} and 6561 to get \frac{1}{81}.

$$\frac{1}{81}$$

Factor

$$\frac{1}{3 ^ {4}} = 0.012345679012345678$$