Solve (frac{-y^-frac{7{6}}}{22y})^2

$$( \frac { - y ^ { - \frac { 7 } { 6 } } } { 22 y } ) ^ { 2 }$$

Evaluate

$$\frac{1}{484y^{\frac{13}{3}}}$$

Solution Steps

To raise \frac{-y^{-\frac{7}{6}}}{22y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-y^{-\frac{7}{6}}\right)^{2}}{\left(22y\right)^{2}}$$

Calculate -y^{-\frac{7}{6}} to the power of 2 and get \left(y^{-\frac{7}{6}}\right)^{2}.

$$\frac{\left(y^{-\frac{7}{6}}\right)^{2}}{\left(22y\right)^{2}}$$

Expand \left(22y\right)^{2}.

$$\frac{\left(y^{-\frac{7}{6}}\right)^{2}}{22^{2}y^{2}}$$

Calculate 22 to the power of 2 and get 484.

$$\frac{\left(y^{-\frac{7}{6}}\right)^{2}}{484y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{7}{6} and 2 to get -\frac{7}{3}.

$$\frac{y^{-\frac{7}{3}}}{484y^{2}}$$

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

$$\frac{1}{484y^{\frac{13}{3}}}$$

Expand

$$\frac{1}{484y^{\frac{13}{3}}}$$

Solution Steps

To raise \frac{-y^{-\frac{7}{6}}}{22y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-y^{-\frac{7}{6}}\right)^{2}}{\left(22y\right)^{2}}$$

Calculate -y^{-\frac{7}{6}} to the power of 2 and get \left(y^{-\frac{7}{6}}\right)^{2}.

$$\frac{\left(y^{-\frac{7}{6}}\right)^{2}}{\left(22y\right)^{2}}$$

Expand \left(22y\right)^{2}.

$$\frac{\left(y^{-\frac{7}{6}}\right)^{2}}{22^{2}y^{2}}$$

Calculate 22 to the power of 2 and get 484.

$$\frac{\left(y^{-\frac{7}{6}}\right)^{2}}{484y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{7}{6} and 2 to get -\frac{7}{3}.

$$\frac{y^{-\frac{7}{3}}}{484y^{2}}$$

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

$$\frac{1}{484y^{\frac{13}{3}}}$$