Solve (2x^0*2x^-2/2x^2)^3

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

Evaluate

$$\frac{8}{x^{12}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and -2 to get -2.

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

Cancel out 2 in both numerator and denominator.

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

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

$$\left(\frac{2}{x^{4}}\right)^{3}$$

To raise \frac{2}{x^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{3}}{\left(x^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{2^{3}}{x^{12}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8}{x^{12}}$$

Expand

$$\frac{8}{x^{12}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and -2 to get -2.

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

Cancel out 2 in both numerator and denominator.

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

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

$$\left(\frac{2}{x^{4}}\right)^{3}$$

To raise \frac{2}{x^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{3}}{\left(x^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{2^{3}}{x^{12}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8}{x^{12}}$$