Solve (7x^-2/xy)^-2

$$( \frac { 7 x ^ { - 2 } } { x y } ) ^ { - 2 }$$

Evaluate

$$\frac{y^{2}x^{6}}{49}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

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

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

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

$$\frac{\frac{1}{49}}{\left(yx^{3}\right)^{-2}}$$

Expand \left(yx^{3}\right)^{-2}.

$$\frac{\frac{1}{49}}{y^{-2}\left(x^{3}\right)^{-2}}$$

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

$$\frac{\frac{1}{49}}{y^{-2}x^{-6}}$$

Express \frac{\frac{1}{49}}{y^{-2}x^{-6}} as a single fraction.

$$\frac{1}{49y^{-2}x^{-6}}$$

Expand

$$\frac{y^{2}x^{6}}{49}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

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

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

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

$$\frac{\frac{1}{49}}{\left(yx^{3}\right)^{-2}}$$

Expand \left(yx^{3}\right)^{-2}.

$$\frac{\frac{1}{49}}{y^{-2}\left(x^{3}\right)^{-2}}$$

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

$$\frac{\frac{1}{49}}{y^{-2}x^{-6}}$$

Express \frac{\frac{1}{49}}{y^{-2}x^{-6}} as a single fraction.

$$\frac{1}{49y^{-2}x^{-6}}$$