Solve (frac{7c^{6}d^4}{8c^4d^4})^-2

$$( \frac { 7 c ^ { 6 } d ^ { 4 } } { 8 c ^ { 4 } d ^ { 4 } } ) ^ { - 2 }$$

Evaluate

$$\frac{64}{49c^{4}}$$

Solution Steps

Cancel out c^{4}d^{4} in both numerator and denominator.

$$\left(\frac{7c^{2}}{8}\right)^{-2}$$

To raise \frac{7c^{2}}{8} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7c^{2}\right)^{-2}}{8^{-2}}$$

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

$$\frac{7^{-2}\left(c^{2}\right)^{-2}}{8^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{7^{-2}c^{-4}}{8^{-2}}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{\frac{1}{49}c^{-4}}{8^{-2}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{49}c^{-4}}{\frac{1}{64}}$$

Divide \frac{1}{49}c^{-4} by \frac{1}{64} by multiplying \frac{1}{49}c^{-4} by the reciprocal of \frac{1}{64}.

$$\frac{1}{49}c^{-4}\times 64$$

Multiply \frac{1}{49} and 64 to get \frac{64}{49}.

$$\frac{64}{49}c^{-4}$$

Expand

$$\frac{64}{49c^{4}}$$

Solution Steps

Cancel out c^{4}d^{4} in both numerator and denominator.

$$\left(\frac{7c^{2}}{8}\right)^{-2}$$

To raise \frac{7c^{2}}{8} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7c^{2}\right)^{-2}}{8^{-2}}$$

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

$$\frac{7^{-2}\left(c^{2}\right)^{-2}}{8^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{7^{-2}c^{-4}}{8^{-2}}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{\frac{1}{49}c^{-4}}{8^{-2}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{49}c^{-4}}{\frac{1}{64}}$$

Divide \frac{1}{49}c^{-4} by \frac{1}{64} by multiplying \frac{1}{49}c^{-4} by the reciprocal of \frac{1}{64}.

$$\frac{1}{49}c^{-4}\times 64$$

Multiply \frac{1}{49} and 64 to get \frac{64}{49}.

$$\frac{64}{49}c^{-4}$$