Solve 3/2*3^2/3+2/2*2^2/7frac{4}{2}*frac{3}{10}*2

$$\frac{ 3 }{ 2 } \times \frac{ { 3 }^{ 2 } }{ 3 } + \frac{ 2 }{ 2 } \times \frac{ { 2 }^{ 2 } }{ 7 } \frac{ 4 }{ 2 } \times \frac{ 3 }{ 10 } \times 2$$

Evaluate

$$\frac{363}{70}\approx 5.185714286$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{3}{2}\times 3^{1}+\frac{2}{2}\times \frac{2^{2}}{7}\times \frac{4}{2}\times \frac{3}{10}\times 2$$

Divide 2 by 2 to get 1.

$$\frac{3}{2}\times 3^{1}+1\times \frac{2^{2}}{7}\times \frac{4}{2}\times \frac{3}{10}\times 2$$

Calculate 3 to the power of 1 and get 3.

$$\frac{3}{2}\times 3+1\times \frac{2^{2}}{7}\times \frac{4}{2}\times \frac{3}{10}\times 2$$

Express \frac{3}{2}\times 3 as a single fraction.

$$\frac{3\times 3}{2}+1\times \frac{2^{2}}{7}\times \frac{4}{2}\times \frac{3}{10}\times 2$$

Multiply 3 and 3 to get 9.

$$\frac{9}{2}+1\times \frac{2^{2}}{7}\times \frac{4}{2}\times \frac{3}{10}\times 2$$

Calculate 2 to the power of 2 and get 4.

$$\frac{9}{2}+1\times \frac{4}{7}\times \frac{4}{2}\times \frac{3}{10}\times 2$$

Multiply 1 and \frac{4}{7} to get \frac{4}{7}.

$$\frac{9}{2}+\frac{4}{7}\times \frac{4}{2}\times \frac{3}{10}\times 2$$

Divide 4 by 2 to get 2.

$$\frac{9}{2}+\frac{4}{7}\times 2\times \frac{3}{10}\times 2$$

Express \frac{4}{7}\times 2 as a single fraction.

$$\frac{9}{2}+\frac{4\times 2}{7}\times \frac{3}{10}\times 2$$

Multiply 4 and 2 to get 8.

$$\frac{9}{2}+\frac{8}{7}\times \frac{3}{10}\times 2$$

Multiply \frac{8}{7} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{2}+\frac{8\times 3}{7\times 10}\times 2$$

Do the multiplications in the fraction \frac{8\times 3}{7\times 10}.

$$\frac{9}{2}+\frac{24}{70}\times 2$$

Reduce the fraction \frac{24}{70} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}+\frac{12}{35}\times 2$$

Express \frac{12}{35}\times 2 as a single fraction.

$$\frac{9}{2}+\frac{12\times 2}{35}$$

Multiply 12 and 2 to get 24.

$$\frac{9}{2}+\frac{24}{35}$$

Least common multiple of 2 and 35 is 70. Convert \frac{9}{2} and \frac{24}{35} to fractions with denominator 70.

$$\frac{315}{70}+\frac{48}{70}$$

Since \frac{315}{70} and \frac{48}{70} have the same denominator, add them by adding their numerators.

$$\frac{315+48}{70}$$

Add 315 and 48 to get 363.

$$\frac{363}{70}$$

Factor

$$\frac{3 \cdot 11 ^ {2}}{2 \cdot 5 \cdot 7} = 5\frac{13}{70} = 5.185714285714286$$