Solve (frac{-21x^{12}y^6}{7x^17y^-2})^3

$$( \frac { - 21 x ^ { 12 } y ^ { 6 } } { 7 x ^ { 17 } y ^ { - 2 } } ) ^ { 3 }$$

Evaluate

$$-\frac{27y^{24}}{x^{15}}$$

Solution Steps

Cancel out 7x^{12} in both numerator and denominator.

$$\left(\frac{-3y^{6}}{y^{-2}x^{5}}\right)^{3}$$

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

$$\left(\frac{-3y^{8}}{x^{5}}\right)^{3}$$

To raise \frac{-3y^{8}}{x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3y^{8}\right)^{3}}{\left(x^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\left(-3y^{8}\right)^{3}}{x^{15}}$$

Expand \left(-3y^{8}\right)^{3}.

$$\frac{\left(-3\right)^{3}\left(y^{8}\right)^{3}}{x^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{\left(-3\right)^{3}y^{24}}{x^{15}}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{-27y^{24}}{x^{15}}$$

Expand

$$-\frac{27y^{24}}{x^{15}}$$

Solution Steps

Cancel out 7x^{12} in both numerator and denominator.

$$\left(\frac{-3y^{6}}{y^{-2}x^{5}}\right)^{3}$$

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

$$\left(\frac{-3y^{8}}{x^{5}}\right)^{3}$$

To raise \frac{-3y^{8}}{x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3y^{8}\right)^{3}}{\left(x^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\left(-3y^{8}\right)^{3}}{x^{15}}$$

Expand \left(-3y^{8}\right)^{3}.

$$\frac{\left(-3\right)^{3}\left(y^{8}\right)^{3}}{x^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{\left(-3\right)^{3}y^{24}}{x^{15}}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{-27y^{24}}{x^{15}}$$