Solve (2e^5f)^4/3edive^4f/3

$$\frac { ( 2 e ^ { 5 } f ) ^ { 4 } } { 3 e } \div \frac { e ^ { 4 } f } { 3 }$$

Evaluate

$$16e^{15}f^{3}$$

Solution Steps

Divide \frac{\left(2e^{5}f\right)^{4}}{3e} by \frac{e^{4}f}{3} by multiplying \frac{\left(2e^{5}f\right)^{4}}{3e} by the reciprocal of \frac{e^{4}f}{3}.

$$\frac{\left(2e^{5}f\right)^{4}\times 3}{3ee^{4}f}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\left(2e^{5}f\right)^{4}}{ee^{4}f}$$

Expand \left(2e^{5}f\right)^{4}.

$$\frac{2^{4}\left(e^{5}\right)^{4}f^{4}}{ee^{4}f}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{2^{4}e^{20}f^{4}}{ee^{4}f}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16e^{20}f^{4}}{ee^{4}f}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{16e^{20}f^{4}}{e^{5}f}$$

Cancel out e^{5}f in both numerator and denominator.

$$16e^{15}f^{3}$$

Expand

$$16e^{15}f^{3}$$

Solution Steps

Divide \frac{\left(2e^{5}f\right)^{4}}{3e} by \frac{e^{4}f}{3} by multiplying \frac{\left(2e^{5}f\right)^{4}}{3e} by the reciprocal of \frac{e^{4}f}{3}.

$$\frac{\left(2e^{5}f\right)^{4}\times 3}{3ee^{4}f}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\left(2e^{5}f\right)^{4}}{ee^{4}f}$$

Expand \left(2e^{5}f\right)^{4}.

$$\frac{2^{4}\left(e^{5}\right)^{4}f^{4}}{ee^{4}f}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{2^{4}e^{20}f^{4}}{ee^{4}f}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16e^{20}f^{4}}{ee^{4}f}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{16e^{20}f^{4}}{e^{5}f}$$

Cancel out e^{5}f in both numerator and denominator.

$$16e^{15}f^{3}$$