Solve [(1/3)^3-(1/9)^3]*3^2quadtext{(f)}12/6^3

$$[ ( \frac { 1 } { 3 } ) ^ { 3 } - ( \frac { 1 } { 9 } ) ^ { 3 } ] \times 3 ^ { 2 } \quad \text { (f) } \frac { 12 } { 6 ^ { 3 } }$$

Evaluate

$$\frac{13f}{729}$$

Solution Steps

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\left(\frac{1}{27}-\left(\frac{1}{9}\right)^{3}\right)\times 3^{2}f\times \frac{12}{6^{3}}$$

Calculate \frac{1}{9} to the power of 3 and get \frac{1}{729}.

$$\left(\frac{1}{27}-\frac{1}{729}\right)\times 3^{2}f\times \frac{12}{6^{3}}$$

Least common multiple of 27 and 729 is 729. Convert \frac{1}{27} and \frac{1}{729} to fractions with denominator 729.

$$\left(\frac{27}{729}-\frac{1}{729}\right)\times 3^{2}f\times \frac{12}{6^{3}}$$

Since \frac{27}{729} and \frac{1}{729} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-1}{729}\times 3^{2}f\times \frac{12}{6^{3}}$$

Subtract 1 from 27 to get 26.

$$\frac{26}{729}\times 3^{2}f\times \frac{12}{6^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{26}{729}\times 9f\times \frac{12}{6^{3}}$$

Express \frac{26}{729}\times 9 as a single fraction.

$$\frac{26\times 9}{729}f\times \frac{12}{6^{3}}$$

Multiply 26 and 9 to get 234.

$$\frac{234}{729}f\times \frac{12}{6^{3}}$$

Reduce the fraction \frac{234}{729} to lowest terms by extracting and canceling out 9.

$$\frac{26}{81}f\times \frac{12}{6^{3}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{26}{81}f\times \frac{12}{216}$$

Reduce the fraction \frac{12}{216} to lowest terms by extracting and canceling out 12.

$$\frac{26}{81}f\times \frac{1}{18}$$

Multiply \frac{26}{81} times \frac{1}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{26\times 1}{81\times 18}f$$

Do the multiplications in the fraction \frac{26\times 1}{81\times 18}.

$$\frac{26}{1458}f$$

Reduce the fraction \frac{26}{1458} to lowest terms by extracting and canceling out 2.

$$\frac{13}{729}f$$

Expand

$$\frac{13f}{729}$$

Solution Steps

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\left(\frac{1}{27}-\left(\frac{1}{9}\right)^{3}\right)\times 3^{2}f\times \frac{12}{6^{3}}$$

Calculate \frac{1}{9} to the power of 3 and get \frac{1}{729}.

$$\left(\frac{1}{27}-\frac{1}{729}\right)\times 3^{2}f\times \frac{12}{6^{3}}$$

Least common multiple of 27 and 729 is 729. Convert \frac{1}{27} and \frac{1}{729} to fractions with denominator 729.

$$\left(\frac{27}{729}-\frac{1}{729}\right)\times 3^{2}f\times \frac{12}{6^{3}}$$

Since \frac{27}{729} and \frac{1}{729} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-1}{729}\times 3^{2}f\times \frac{12}{6^{3}}$$

Subtract 1 from 27 to get 26.

$$\frac{26}{729}\times 3^{2}f\times \frac{12}{6^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{26}{729}\times 9f\times \frac{12}{6^{3}}$$

Express \frac{26}{729}\times 9 as a single fraction.

$$\frac{26\times 9}{729}f\times \frac{12}{6^{3}}$$

Multiply 26 and 9 to get 234.

$$\frac{234}{729}f\times \frac{12}{6^{3}}$$

Reduce the fraction \frac{234}{729} to lowest terms by extracting and canceling out 9.

$$\frac{26}{81}f\times \frac{12}{6^{3}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{26}{81}f\times \frac{12}{216}$$

Reduce the fraction \frac{12}{216} to lowest terms by extracting and canceling out 12.

$$\frac{26}{81}f\times \frac{1}{18}$$

Multiply \frac{26}{81} times \frac{1}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{26\times 1}{81\times 18}f$$

Do the multiplications in the fraction \frac{26\times 1}{81\times 18}.

$$\frac{26}{1458}f$$

Reduce the fraction \frac{26}{1458} to lowest terms by extracting and canceling out 2.

$$\frac{13}{729}f$$