Solve frac{(3e^{2}f)^{3}*(3ef^2)^2}{8e^2f^3}

$$\frac { ( 3 e ^ { 2 } f ) ^ { 3 } \times ( 3 e f ^ { 2 } ) ^ { 2 } } { 8 e ^ { 2 } f ^ { 3 } }$$

Evaluate

$$\frac{243e^{6}f^{4}}{8}$$

Solution Steps

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

$$\frac{3^{3}\left(e^{2}\right)^{3}f^{3}\times \left(3ef^{2}\right)^{2}}{8e^{2}f^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{3^{3}e^{6}f^{3}\times \left(3ef^{2}\right)^{2}}{8e^{2}f^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27e^{6}f^{3}\times \left(3ef^{2}\right)^{2}}{8e^{2}f^{3}}$$

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

$$\frac{27e^{6}f^{3}\times 3^{2}e^{2}\left(f^{2}\right)^{2}}{8e^{2}f^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{27e^{6}f^{3}\times 3^{2}e^{2}f^{4}}{8e^{2}f^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{27e^{6}f^{3}\times 9e^{2}f^{4}}{8e^{2}f^{3}}$$

Multiply 27 and 9 to get 243.

$$\frac{243e^{6}f^{3}e^{2}f^{4}}{8e^{2}f^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{243e^{8}f^{3}f^{4}}{8e^{2}f^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{243e^{8}f^{7}}{8e^{2}f^{3}}$$

Cancel out e^{2}f^{3} in both numerator and denominator.

$$\frac{243e^{6}f^{4}}{8}$$

Expand

$$\frac{243e^{6}f^{4}}{8}$$

Solution Steps

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

$$\frac{3^{3}\left(e^{2}\right)^{3}f^{3}\times \left(3ef^{2}\right)^{2}}{8e^{2}f^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{3^{3}e^{6}f^{3}\times \left(3ef^{2}\right)^{2}}{8e^{2}f^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27e^{6}f^{3}\times \left(3ef^{2}\right)^{2}}{8e^{2}f^{3}}$$

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

$$\frac{27e^{6}f^{3}\times 3^{2}e^{2}\left(f^{2}\right)^{2}}{8e^{2}f^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{27e^{6}f^{3}\times 3^{2}e^{2}f^{4}}{8e^{2}f^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{27e^{6}f^{3}\times 9e^{2}f^{4}}{8e^{2}f^{3}}$$

Multiply 27 and 9 to get 243.

$$\frac{243e^{6}f^{3}e^{2}f^{4}}{8e^{2}f^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{243e^{8}f^{3}f^{4}}{8e^{2}f^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{243e^{8}f^{7}}{8e^{2}f^{3}}$$

Cancel out e^{2}f^{3} in both numerator and denominator.

$$\frac{243e^{6}f^{4}}{8}$$