Solve (-7/2xy^-1)^-2

$$( - \frac { 7 } { 2 } x y ^ { - 1 } ) ^ { - 2 }$$

Evaluate

$$\frac{4\times \left(\frac{y}{x}\right)^{2}}{49}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{7}{2}x^{1}\times \frac{1}{y}\right)^{-2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-\frac{7}{2}\right)^{-2}\left(x^{1}\right)^{-2}\times \left(\frac{1}{y}\right)^{-2}$$

Raise -\frac{7}{2} to the power -2.

$$\frac{4}{49}\left(x^{1}\right)^{-2}\times \left(\frac{1}{y}\right)^{-2}$$

To raise a power to another power, multiply the exponents.

$$\frac{4}{49}x^{-2}y^{-\left(-2\right)}$$

Multiply -1 times -2.

$$\frac{4}{49}\times \frac{1}{x^{2}}y^{2}$$

Expand

$$\frac{4\times \left(\frac{y}{x}\right)^{2}}{49}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{7}{2}x^{1}\times \frac{1}{y}\right)^{-2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-\frac{7}{2}\right)^{-2}\left(x^{1}\right)^{-2}\times \left(\frac{1}{y}\right)^{-2}$$

Raise -\frac{7}{2} to the power -2.

$$\frac{4}{49}\left(x^{1}\right)^{-2}\times \left(\frac{1}{y}\right)^{-2}$$

To raise a power to another power, multiply the exponents.

$$\frac{4}{49}x^{-2}y^{-\left(-2\right)}$$

Multiply -1 times -2.

$$\frac{4}{49}\times \frac{1}{x^{2}}y^{2}$$