Solve (frac{9b^{4}}{8b^{3}})^2(2b^4/3b^3)^3=

$$( \frac { 9 b ^ { 4 } } { 8 b ^ { 3 } } ) ^ { 2 } ( \frac { 2 b ^ { 4 } } { 3 b ^ { 3 } } ) ^ { 3 } =$$

Evaluate

$$\frac{3b^{5}}{8}$$

Solution Steps

Cancel out b^{3} in both numerator and denominator.

$$\left(\frac{9b}{8}\right)^{2}\times \left(\frac{2b^{4}}{3b^{3}}\right)^{3}$$

To raise \frac{9b}{8} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9b\right)^{2}}{8^{2}}\times \left(\frac{2b^{4}}{3b^{3}}\right)^{3}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{\left(9b\right)^{2}}{8^{2}}\times \left(\frac{2b}{3}\right)^{3}$$

To raise \frac{2b}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9b\right)^{2}}{8^{2}}\times \frac{\left(2b\right)^{3}}{3^{3}}$$

Multiply \frac{\left(9b\right)^{2}}{8^{2}} times \frac{\left(2b\right)^{3}}{3^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9b\right)^{2}\times \left(2b\right)^{3}}{8^{2}\times 3^{3}}$$

Expand \left(9b\right)^{2}.

$$\frac{9^{2}b^{2}\times \left(2b\right)^{3}}{8^{2}\times 3^{3}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{81b^{2}\times \left(2b\right)^{3}}{8^{2}\times 3^{3}}$$

Expand \left(2b\right)^{3}.

$$\frac{81b^{2}\times 2^{3}b^{3}}{8^{2}\times 3^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{81b^{2}\times 8b^{3}}{8^{2}\times 3^{3}}$$

Multiply 81 and 8 to get 648.

$$\frac{648b^{2}b^{3}}{8^{2}\times 3^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{648b^{5}}{8^{2}\times 3^{3}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{648b^{5}}{64\times 3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{648b^{5}}{64\times 27}$$

Multiply 64 and 27 to get 1728.

$$\frac{648b^{5}}{1728}$$

Divide 648b^{5} by 1728 to get \frac{3}{8}b^{5}.

$$\frac{3}{8}b^{5}$$

Expand

$$\frac{3b^{5}}{8}$$

Solution Steps

Cancel out b^{3} in both numerator and denominator.

$$\left(\frac{9b}{8}\right)^{2}\times \left(\frac{2b^{4}}{3b^{3}}\right)^{3}$$

To raise \frac{9b}{8} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9b\right)^{2}}{8^{2}}\times \left(\frac{2b^{4}}{3b^{3}}\right)^{3}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{\left(9b\right)^{2}}{8^{2}}\times \left(\frac{2b}{3}\right)^{3}$$

To raise \frac{2b}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9b\right)^{2}}{8^{2}}\times \frac{\left(2b\right)^{3}}{3^{3}}$$

Multiply \frac{\left(9b\right)^{2}}{8^{2}} times \frac{\left(2b\right)^{3}}{3^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9b\right)^{2}\times \left(2b\right)^{3}}{8^{2}\times 3^{3}}$$

Expand \left(9b\right)^{2}.

$$\frac{9^{2}b^{2}\times \left(2b\right)^{3}}{8^{2}\times 3^{3}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{81b^{2}\times \left(2b\right)^{3}}{8^{2}\times 3^{3}}$$

Expand \left(2b\right)^{3}.

$$\frac{81b^{2}\times 2^{3}b^{3}}{8^{2}\times 3^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{81b^{2}\times 8b^{3}}{8^{2}\times 3^{3}}$$

Multiply 81 and 8 to get 648.

$$\frac{648b^{2}b^{3}}{8^{2}\times 3^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{648b^{5}}{8^{2}\times 3^{3}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{648b^{5}}{64\times 3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{648b^{5}}{64\times 27}$$

Multiply 64 and 27 to get 1728.

$$\frac{648b^{5}}{1728}$$

Divide 648b^{5} by 1728 to get \frac{3}{8}b^{5}.

$$\frac{3}{8}b^{5}$$