Solve {left(frac{-{y}^frac{3{2}}}{{y}^-frac{1{3}}}right)}^3

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

Evaluate

$$-y^{\frac{11}{2}}$$

Solution Steps

To raise \frac{-y^{\frac{3}{2}}}{y^{-\frac{1}{3}}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{3} and 3 to get -1.

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

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

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

To raise a power to another power, multiply the exponents. Multiply \frac{3}{2} and 3 to get \frac{9}{2}.

$$\frac{\left(-1\right)^{3}y^{\frac{9}{2}}}{y^{-1}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{-y^{\frac{9}{2}}}{y^{-1}}$$

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

$$-y^{\frac{11}{2}}$$

Expand

$$-y^{\frac{11}{2}}$$

Solution Steps

To raise \frac{-y^{\frac{3}{2}}}{y^{-\frac{1}{3}}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{3} and 3 to get -1.

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

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

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

To raise a power to another power, multiply the exponents. Multiply \frac{3}{2} and 3 to get \frac{9}{2}.

$$\frac{\left(-1\right)^{3}y^{\frac{9}{2}}}{y^{-1}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{-y^{\frac{9}{2}}}{y^{-1}}$$

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

$$-y^{\frac{11}{2}}$$