Solve (7x^-2y/x^8y^-5)^3=

$$( \frac { 7 x ^ { - 2 } y } { x ^ { 8 } y ^ { - 5 } } ) ^ { 3 } =$$

Evaluate

$$\frac{343y^{18}}{x^{30}}$$

Solution Steps

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

$$\left(\frac{7x^{-2}y^{6}}{x^{8}}\right)^{3}$$

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

$$\left(\frac{7y^{6}}{x^{10}}\right)^{3}$$

To raise \frac{7y^{6}}{x^{10}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7y^{6}\right)^{3}}{\left(x^{10}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 3 to get 30.

$$\frac{\left(7y^{6}\right)^{3}}{x^{30}}$$

Expand \left(7y^{6}\right)^{3}.

$$\frac{7^{3}\left(y^{6}\right)^{3}}{x^{30}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{7^{3}y^{18}}{x^{30}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{343y^{18}}{x^{30}}$$

Expand

$$\frac{343y^{18}}{x^{30}}$$

Solution Steps

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

$$\left(\frac{7x^{-2}y^{6}}{x^{8}}\right)^{3}$$

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

$$\left(\frac{7y^{6}}{x^{10}}\right)^{3}$$

To raise \frac{7y^{6}}{x^{10}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7y^{6}\right)^{3}}{\left(x^{10}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 3 to get 30.

$$\frac{\left(7y^{6}\right)^{3}}{x^{30}}$$

Expand \left(7y^{6}\right)^{3}.

$$\frac{7^{3}\left(y^{6}\right)^{3}}{x^{30}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{7^{3}y^{18}}{x^{30}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{343y^{18}}{x^{30}}$$