Solve (5x^7/12x^9)^-2

$$( \frac { 5 x ^ { 7 } } { 12 x ^ { 9 } } ) ^ { - 2 }$$

Evaluate

$$\frac{144x^{4}}{25}$$

Solution Steps

Cancel out x^{7} in both numerator and denominator.

$$\left(\frac{5}{12x^{2}}\right)^{-2}$$

To raise \frac{5}{12x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{5^{-2}}{\left(12x^{2}\right)^{-2}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}}{\left(12x^{2}\right)^{-2}}$$

Expand \left(12x^{2}\right)^{-2}.

$$\frac{\frac{1}{25}}{12^{-2}\left(x^{2}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}}{12^{-2}x^{-4}}$$

Calculate 12 to the power of -2 and get \frac{1}{144}.

$$\frac{\frac{1}{25}}{\frac{1}{144}x^{-4}}$$

Express \frac{\frac{1}{25}}{\frac{1}{144}x^{-4}} as a single fraction.

$$\frac{1}{25\times \frac{1}{144}x^{-4}}$$

Multiply 25 and \frac{1}{144} to get \frac{25}{144}.

$$\frac{1}{\frac{25}{144}x^{-4}}$$

Expand

$$\frac{144x^{4}}{25}$$

Solution Steps

Cancel out x^{7} in both numerator and denominator.

$$\left(\frac{5}{12x^{2}}\right)^{-2}$$

To raise \frac{5}{12x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{5^{-2}}{\left(12x^{2}\right)^{-2}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}}{\left(12x^{2}\right)^{-2}}$$

Expand \left(12x^{2}\right)^{-2}.

$$\frac{\frac{1}{25}}{12^{-2}\left(x^{2}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}}{12^{-2}x^{-4}}$$

Calculate 12 to the power of -2 and get \frac{1}{144}.

$$\frac{\frac{1}{25}}{\frac{1}{144}x^{-4}}$$

Express \frac{\frac{1}{25}}{\frac{1}{144}x^{-4}} as a single fraction.

$$\frac{1}{25\times \frac{1}{144}x^{-4}}$$

Multiply 25 and \frac{1}{144} to get \frac{25}{144}.

$$\frac{1}{\frac{25}{144}x^{-4}}$$