Solve (-y^312/y^-1/3)^3

$$( \frac { - y ^ { 312 } } { y ^ { - 1 / 3 } } ) ^ { 3 }$$

Evaluate

$$-y^{937}$$

Solution Steps

To raise \frac{-y^{312}}{y^{-\frac{1}{3}}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-y^{312}\right)^{3}}{\left(y^{-\frac{1}{3}}\right)^{3}}$$

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

$$\frac{\left(-y^{312}\right)^{3}}{y^{-1}}$$

Expand \left(-y^{312}\right)^{3}.

$$\frac{\left(-1\right)^{3}\left(y^{312}\right)^{3}}{y^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 312 and 3 to get 936.

$$\frac{\left(-1\right)^{3}y^{936}}{y^{-1}}$$

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

$$\frac{-y^{936}}{y^{-1}}$$

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

$$-y^{937}$$

Expand

$$-y^{937}$$

Solution Steps

To raise \frac{-y^{312}}{y^{-\frac{1}{3}}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-y^{312}\right)^{3}}{\left(y^{-\frac{1}{3}}\right)^{3}}$$

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

$$\frac{\left(-y^{312}\right)^{3}}{y^{-1}}$$

Expand \left(-y^{312}\right)^{3}.

$$\frac{\left(-1\right)^{3}\left(y^{312}\right)^{3}}{y^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 312 and 3 to get 936.

$$\frac{\left(-1\right)^{3}y^{936}}{y^{-1}}$$

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

$$\frac{-y^{936}}{y^{-1}}$$

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

$$-y^{937}$$