Solve {left(4x^-1y^-40/2^-2x^4{y^-10}right)}^-2

$${ \left( \frac{ 4 { x }^{ -1 } { y }^{ -40 } }{ { 2 }^{ -2 } { x }^{ 4 } { y }^{ -10 } } \right) }^{ -2 }$$

Evaluate

$$\frac{x^{10}y^{60}}{256}$$

Solution Steps

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

$$\left(\frac{4}{2^{-2}x^{5}y^{30}}\right)^{-2}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\left(\frac{4}{\frac{1}{4}x^{5}y^{30}}\right)^{-2}$$

To raise \frac{4}{\frac{1}{4}x^{5}y^{30}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{4^{-2}}{\left(\frac{1}{4}x^{5}y^{30}\right)^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\left(\frac{1}{4}x^{5}y^{30}\right)^{-2}}$$

Expand \left(\frac{1}{4}x^{5}y^{30}\right)^{-2}.

$$\frac{\frac{1}{16}}{\left(\frac{1}{4}\right)^{-2}\left(x^{5}\right)^{-2}\left(y^{30}\right)^{-2}}$$

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

$$\frac{\frac{1}{16}}{\left(\frac{1}{4}\right)^{-2}x^{-10}\left(y^{30}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 30 and -2 to get -60.

$$\frac{\frac{1}{16}}{\left(\frac{1}{4}\right)^{-2}x^{-10}y^{-60}}$$

Calculate \frac{1}{4} to the power of -2 and get 16.

$$\frac{\frac{1}{16}}{16x^{-10}y^{-60}}$$

Express \frac{\frac{1}{16}}{16x^{-10}y^{-60}} as a single fraction.

$$\frac{1}{16\times 16x^{-10}y^{-60}}$$

Multiply 16 and 16 to get 256.

$$\frac{1}{256x^{-10}y^{-60}}$$

Expand

$$\frac{x^{10}y^{60}}{256}$$

Solution Steps

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

$$\left(\frac{4}{2^{-2}x^{5}y^{30}}\right)^{-2}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\left(\frac{4}{\frac{1}{4}x^{5}y^{30}}\right)^{-2}$$

To raise \frac{4}{\frac{1}{4}x^{5}y^{30}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{4^{-2}}{\left(\frac{1}{4}x^{5}y^{30}\right)^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\left(\frac{1}{4}x^{5}y^{30}\right)^{-2}}$$

Expand \left(\frac{1}{4}x^{5}y^{30}\right)^{-2}.

$$\frac{\frac{1}{16}}{\left(\frac{1}{4}\right)^{-2}\left(x^{5}\right)^{-2}\left(y^{30}\right)^{-2}}$$

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

$$\frac{\frac{1}{16}}{\left(\frac{1}{4}\right)^{-2}x^{-10}\left(y^{30}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 30 and -2 to get -60.

$$\frac{\frac{1}{16}}{\left(\frac{1}{4}\right)^{-2}x^{-10}y^{-60}}$$

Calculate \frac{1}{4} to the power of -2 and get 16.

$$\frac{\frac{1}{16}}{16x^{-10}y^{-60}}$$

Express \frac{\frac{1}{16}}{16x^{-10}y^{-60}} as a single fraction.

$$\frac{1}{16\times 16x^{-10}y^{-60}}$$

Multiply 16 and 16 to get 256.

$$\frac{1}{256x^{-10}y^{-60}}$$