Solve (frac{2^{-3}x^{2}y^{4}}{2^-1x^4y^8})^-3

$$( \frac { 2 ^ { - 3 } x ^ { 2 } y ^ { 4 } } { 2 ^ { - 1 } x ^ { 4 } y ^ { 8 } } ) ^ { - 3 }$$

Evaluate

$$64x^{6}y^{12}$$

Solution Steps

Cancel out x^{2}y^{4} in both numerator and denominator.

$$\left(\frac{2^{-3}}{\frac{1}{2}x^{2}y^{4}}\right)^{-3}$$

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

$$\left(\frac{1}{2^{2}x^{2}y^{4}}\right)^{-3}$$

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{1}{4x^{2}y^{4}}\right)^{-3}$$

To raise \frac{1}{4x^{2}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-3}}{\left(4x^{2}y^{4}\right)^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{1}{\left(4x^{2}y^{4}\right)^{-3}}$$

Expand \left(4x^{2}y^{4}\right)^{-3}.

$$\frac{1}{4^{-3}\left(x^{2}\right)^{-3}\left(y^{4}\right)^{-3}}$$

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

$$\frac{1}{4^{-3}x^{-6}\left(y^{4}\right)^{-3}}$$

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

$$\frac{1}{4^{-3}x^{-6}y^{-12}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{1}{\frac{1}{64}x^{-6}y^{-12}}$$

Expand

$$64x^{6}y^{12}$$

Solution Steps

Cancel out x^{2}y^{4} in both numerator and denominator.

$$\left(\frac{2^{-3}}{\frac{1}{2}x^{2}y^{4}}\right)^{-3}$$

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

$$\left(\frac{1}{2^{2}x^{2}y^{4}}\right)^{-3}$$

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{1}{4x^{2}y^{4}}\right)^{-3}$$

To raise \frac{1}{4x^{2}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-3}}{\left(4x^{2}y^{4}\right)^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{1}{\left(4x^{2}y^{4}\right)^{-3}}$$

Expand \left(4x^{2}y^{4}\right)^{-3}.

$$\frac{1}{4^{-3}\left(x^{2}\right)^{-3}\left(y^{4}\right)^{-3}}$$

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

$$\frac{1}{4^{-3}x^{-6}\left(y^{4}\right)^{-3}}$$

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

$$\frac{1}{4^{-3}x^{-6}y^{-12}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{1}{\frac{1}{64}x^{-6}y^{-12}}$$