Solve (4de^3)^2div9d^4e=

$$( 4 d e ^ { 3 } ) ^ { 2 } \div 9 d ^ { 4 } e =$$

Evaluate

$$\frac{16e^{7}d^{6}}{9}$$

Solution Steps

Expand \left(4de^{3}\right)^{2}.

$$\frac{4^{2}d^{2}\left(e^{3}\right)^{2}}{9}d^{4}e$$

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

$$\frac{4^{2}d^{2}e^{6}}{9}d^{4}e$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16d^{2}e^{6}}{9}d^{4}e$$

Express \frac{16d^{2}e^{6}}{9}d^{4} as a single fraction.

$$\frac{16d^{2}e^{6}d^{4}}{9}e$$

Express \frac{16d^{2}e^{6}d^{4}}{9}e as a single fraction.

$$\frac{16d^{2}e^{6}d^{4}e}{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{16d^{6}e^{6}e}{9}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{16d^{6}e^{7}}{9}$$

Expand

$$\frac{16e^{7}d^{6}}{9}$$

Solution Steps

Expand \left(4de^{3}\right)^{2}.

$$\frac{4^{2}d^{2}\left(e^{3}\right)^{2}}{9}d^{4}e$$

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

$$\frac{4^{2}d^{2}e^{6}}{9}d^{4}e$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16d^{2}e^{6}}{9}d^{4}e$$

Express \frac{16d^{2}e^{6}}{9}d^{4} as a single fraction.

$$\frac{16d^{2}e^{6}d^{4}}{9}e$$

Express \frac{16d^{2}e^{6}d^{4}}{9}e as a single fraction.

$$\frac{16d^{2}e^{6}d^{4}e}{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{16d^{6}e^{6}e}{9}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{16d^{6}e^{7}}{9}$$