Solve c^4c^3/cd^2{left(d^2/{c^3}right)}^3

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

Evaluate

$$\frac{d^{4}}{c^{3}}$$

Solution Steps

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

$$\frac{c^{7}}{cd^{2}}\times \left(\frac{d^{2}}{c^{3}}\right)^{3}$$

Cancel out c in both numerator and denominator.

$$\frac{c^{6}}{d^{2}}\times \left(\frac{d^{2}}{c^{3}}\right)^{3}$$

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

$$\frac{c^{6}}{d^{2}}\times \frac{\left(d^{2}\right)^{3}}{\left(c^{3}\right)^{3}}$$

Multiply \frac{c^{6}}{d^{2}} times \frac{\left(d^{2}\right)^{3}}{\left(c^{3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{c^{6}\left(d^{2}\right)^{3}}{d^{2}\left(c^{3}\right)^{3}}$$

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

$$\frac{c^{6}d^{6}}{d^{2}\left(c^{3}\right)^{3}}$$

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

$$\frac{c^{6}d^{6}}{d^{2}c^{9}}$$

Cancel out d^{2}c^{6} in both numerator and denominator.

$$\frac{d^{4}}{c^{3}}$$

Expand

$$\frac{d^{4}}{c^{3}}$$

Solution Steps

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

$$\frac{c^{7}}{cd^{2}}\times \left(\frac{d^{2}}{c^{3}}\right)^{3}$$

Cancel out c in both numerator and denominator.

$$\frac{c^{6}}{d^{2}}\times \left(\frac{d^{2}}{c^{3}}\right)^{3}$$

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

$$\frac{c^{6}}{d^{2}}\times \frac{\left(d^{2}\right)^{3}}{\left(c^{3}\right)^{3}}$$

Multiply \frac{c^{6}}{d^{2}} times \frac{\left(d^{2}\right)^{3}}{\left(c^{3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{c^{6}\left(d^{2}\right)^{3}}{d^{2}\left(c^{3}\right)^{3}}$$

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

$$\frac{c^{6}d^{6}}{d^{2}\left(c^{3}\right)^{3}}$$

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

$$\frac{c^{6}d^{6}}{d^{2}c^{9}}$$

Cancel out d^{2}c^{6} in both numerator and denominator.

$$\frac{d^{4}}{c^{3}}$$