Solve (6c^2c^5/3d^-3)^2

$$( \frac { 6 c ^ { 2 } c ^ { 5 } } { 3 d ^ { - 3 } } ) ^ { 2 }$$

Evaluate

$$4d^{6}c^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\left(\frac{6c^{7}}{3d^{-3}}\right)^{2}$$

Cancel out 3 in both numerator and denominator.

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

To raise \frac{2c^{7}}{d^{-3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(2c^{7}\right)^{2}}{d^{-6}}$$

Expand \left(2c^{7}\right)^{2}.

$$\frac{2^{2}\left(c^{7}\right)^{2}}{d^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{2^{2}c^{14}}{d^{-6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4c^{14}}{d^{-6}}$$

Expand

$$4d^{6}c^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\left(\frac{6c^{7}}{3d^{-3}}\right)^{2}$$

Cancel out 3 in both numerator and denominator.

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

To raise \frac{2c^{7}}{d^{-3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(2c^{7}\right)^{2}}{d^{-6}}$$

Expand \left(2c^{7}\right)^{2}.

$$\frac{2^{2}\left(c^{7}\right)^{2}}{d^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{2^{2}c^{14}}{d^{-6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4c^{14}}{d^{-6}}$$