Solve (x^-2/2x^-7y^-2)^3

$$( \frac { x ^ { - 2 } } { 2 x ^ { - 7 } y ^ { - 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{y^{6}x^{15}}{8}$$

Solution Steps

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

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

To raise \frac{x^{5}}{2y^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{x^{15}}{\left(2y^{-2}\right)^{3}}$$

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

$$\frac{x^{15}}{2^{3}\left(y^{-2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{x^{15}}{2^{3}y^{-6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{x^{15}}{8y^{-6}}$$

Expand

$$\frac{y^{6}x^{15}}{8}$$

Solution Steps

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

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

To raise \frac{x^{5}}{2y^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{x^{15}}{\left(2y^{-2}\right)^{3}}$$

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

$$\frac{x^{15}}{2^{3}\left(y^{-2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{x^{15}}{2^{3}y^{-6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{x^{15}}{8y^{-6}}$$