Solve frac{x^{-8}}{8y}(frac{2x^{-2}y^2}{x^-3y^4})^3

$$\frac { x ^ { - 8 } } { 8 y } ( \frac { 2 x ^ { - 2 } y ^ { 2 } } { x ^ { - 3 } y ^ { 4 } } ) ^ { 3 }$$

Evaluate

$$\frac{1}{x^{5}y^{7}}$$

Solution Steps

Cancel out y^{2} in both numerator and denominator.

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

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

$$\frac{x^{-8}}{8y}\times \left(\frac{2x^{1}}{y^{2}}\right)^{3}$$

Calculate x to the power of 1 and get x.

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

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

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

Multiply \frac{x^{-8}}{8y} times \frac{\left(2x\right)^{3}}{\left(y^{2}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

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

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

$$\frac{x^{-8}\times 2^{3}x^{3}}{8y^{7}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{x^{-8}\times 8x^{3}}{8y^{7}}$$

To multiply powers of the same base, add their exponents. Add -8 and 3 to get -5.

$$\frac{x^{-5}\times 8}{8y^{7}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{x^{-5}}{y^{7}}$$

Expand

$$\frac{1}{x^{5}y^{7}}$$

Solution Steps

Cancel out y^{2} in both numerator and denominator.

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

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

$$\frac{x^{-8}}{8y}\times \left(\frac{2x^{1}}{y^{2}}\right)^{3}$$

Calculate x to the power of 1 and get x.

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

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

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

Multiply \frac{x^{-8}}{8y} times \frac{\left(2x\right)^{3}}{\left(y^{2}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

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

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

$$\frac{x^{-8}\times 2^{3}x^{3}}{8y^{7}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{x^{-8}\times 8x^{3}}{8y^{7}}$$

To multiply powers of the same base, add their exponents. Add -8 and 3 to get -5.

$$\frac{x^{-5}\times 8}{8y^{7}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{x^{-5}}{y^{7}}$$