Solve (frac{2^{-1}x^{-2}y^{0}}{8^-2x^3y^4})^-2

$$( \frac { 2 ^ { - 1 } x ^ { - 2 } y ^ { 0 } } { 8 ^ { - 2 } x ^ { 3 } y ^ { 4 } } ) ^ { - 2 }$$

Evaluate

$$\frac{y^{8}x^{10}}{1024}$$

Solution Steps

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

$$\left(\frac{\frac{1}{2}}{8^{-2}y^{4}x^{5}}\right)^{-2}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\left(\frac{\frac{1}{2}}{\frac{1}{64}y^{4}x^{5}}\right)^{-2}$$

Express \frac{\frac{1}{2}}{\frac{1}{64}y^{4}x^{5}} as a single fraction.

$$\left(\frac{1}{2\times \frac{1}{64}y^{4}x^{5}}\right)^{-2}$$

Multiply 2 and \frac{1}{64} to get \frac{1}{32}.

$$\left(\frac{1}{\frac{1}{32}y^{4}x^{5}}\right)^{-2}$$

To raise \frac{1}{\frac{1}{32}y^{4}x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-2}}{\left(\frac{1}{32}y^{4}x^{5}\right)^{-2}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{1}{\left(\frac{1}{32}y^{4}x^{5}\right)^{-2}}$$

Expand \left(\frac{1}{32}y^{4}x^{5}\right)^{-2}.

$$\frac{1}{\left(\frac{1}{32}\right)^{-2}\left(y^{4}\right)^{-2}\left(x^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{1}{\left(\frac{1}{32}\right)^{-2}y^{-8}\left(x^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{1}{\left(\frac{1}{32}\right)^{-2}y^{-8}x^{-10}}$$

Calculate \frac{1}{32} to the power of -2 and get 1024.

$$\frac{1}{1024y^{-8}x^{-10}}$$

Expand

$$\frac{y^{8}x^{10}}{1024}$$

Solution Steps

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

$$\left(\frac{\frac{1}{2}}{8^{-2}y^{4}x^{5}}\right)^{-2}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\left(\frac{\frac{1}{2}}{\frac{1}{64}y^{4}x^{5}}\right)^{-2}$$

Express \frac{\frac{1}{2}}{\frac{1}{64}y^{4}x^{5}} as a single fraction.

$$\left(\frac{1}{2\times \frac{1}{64}y^{4}x^{5}}\right)^{-2}$$

Multiply 2 and \frac{1}{64} to get \frac{1}{32}.

$$\left(\frac{1}{\frac{1}{32}y^{4}x^{5}}\right)^{-2}$$

To raise \frac{1}{\frac{1}{32}y^{4}x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-2}}{\left(\frac{1}{32}y^{4}x^{5}\right)^{-2}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{1}{\left(\frac{1}{32}y^{4}x^{5}\right)^{-2}}$$

Expand \left(\frac{1}{32}y^{4}x^{5}\right)^{-2}.

$$\frac{1}{\left(\frac{1}{32}\right)^{-2}\left(y^{4}\right)^{-2}\left(x^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{1}{\left(\frac{1}{32}\right)^{-2}y^{-8}\left(x^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{1}{\left(\frac{1}{32}\right)^{-2}y^{-8}x^{-10}}$$

Calculate \frac{1}{32} to the power of -2 and get 1024.

$$\frac{1}{1024y^{-8}x^{-10}}$$