Solve (frac{2^{0}x^{3}y^-2}{x^2y^6})^3

$$( \frac { 2 ^ { 0 } x ^ { 3 } y ^ { - 2 } } { x ^ { 2 } y ^ { 6 } } ) ^ { 3 }$$

Evaluate

$$\frac{x^{3}}{y^{24}}$$

Short Solution Steps

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

$$\left(\frac{2^{0}y^{-2}x}{y^{6}}\right)^{3}$$

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

$$\left(\frac{2^{0}x}{y^{8}}\right)^{3}$$

Calculate 2 to the power of 0 and get 1.

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

To raise \frac{1x}{y^{8}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(1x\right)^{3}}{y^{24}}$$

Expand \left(1x\right)^{3}.

$$\frac{1^{3}x^{3}}{y^{24}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1x^{3}}{y^{24}}$$

For any term t, t\times 1=t and 1t=t.

$$\frac{x^{3}}{y^{24}}$$

Expand

$$\frac{x^{3}}{y^{24}}$$

Short Solution Steps

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

$$\left(\frac{2^{0}y^{-2}x}{y^{6}}\right)^{3}$$

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

$$\left(\frac{2^{0}x}{y^{8}}\right)^{3}$$

Calculate 2 to the power of 0 and get 1.

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

To raise \frac{1x}{y^{8}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(1x\right)^{3}}{y^{24}}$$

Expand \left(1x\right)^{3}.

$$\frac{1^{3}x^{3}}{y^{24}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1x^{3}}{y^{24}}$$

For any term t, t\times 1=t and 1t=t.

$$\frac{x^{3}}{y^{24}}$$