Solve (frac{e^{4}d^{3}}{ed^2})(d^2/c^3)^3

$$( \frac { e ^ { 4 } d ^ { 3 } } { e d ^ { 2 } } ) ( \frac { d ^ { 2 } } { c ^ { 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{e^{3}d^{7}}{c^{9}}$$

Solution Steps

Cancel out ed^{2} in both numerator and denominator.

$$e^{3}d\times \left(\frac{d^{2}}{c^{3}}\right)^{3}$$

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

$$e^{3}d\times \frac{\left(d^{2}\right)^{3}}{\left(c^{3}\right)^{3}}$$

Express e^{3}\times \frac{\left(d^{2}\right)^{3}}{\left(c^{3}\right)^{3}} as a single fraction.

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

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

$$\frac{e^{3}d^{6}}{\left(c^{3}\right)^{3}}d$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{e^{3}d^{6}}{c^{9}}d$$

Express \frac{e^{3}d^{6}}{c^{9}}d as a single fraction.

$$\frac{e^{3}d^{6}d}{c^{9}}$$

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

$$\frac{e^{3}d^{7}}{c^{9}}$$

Expand

$$\frac{e^{3}d^{7}}{c^{9}}$$

Solution Steps

Cancel out ed^{2} in both numerator and denominator.

$$e^{3}d\times \left(\frac{d^{2}}{c^{3}}\right)^{3}$$

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

$$e^{3}d\times \frac{\left(d^{2}\right)^{3}}{\left(c^{3}\right)^{3}}$$

Express e^{3}\times \frac{\left(d^{2}\right)^{3}}{\left(c^{3}\right)^{3}} as a single fraction.

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

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

$$\frac{e^{3}d^{6}}{\left(c^{3}\right)^{3}}d$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{e^{3}d^{6}}{c^{9}}d$$

Express \frac{e^{3}d^{6}}{c^{9}}d as a single fraction.

$$\frac{e^{3}d^{6}d}{c^{9}}$$

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

$$\frac{e^{3}d^{7}}{c^{9}}$$