Solve (frac{2x^{-4}y^{8}}{16xy^{-3}})^-2(x^2y^2)^-1

$$( \frac { 2 x ^ { - 4 } y ^ { 8 } } { 16 x y ^ { - 3 } } ) ^ { - 2 } ( x ^ { 2 } y ^ { 2 } ) ^ { - 1 }$$

Evaluate

$$\frac{64x^{8}}{y^{24}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

$$\left(\frac{x^{-4}y^{11}}{8x}\right)^{-2}\left(x^{2}y^{2}\right)^{-1}$$

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

$$\left(\frac{y^{11}}{8x^{5}}\right)^{-2}\left(x^{2}y^{2}\right)^{-1}$$

To raise \frac{y^{11}}{8x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}\left(x^{2}y^{2}\right)^{-1}$$

Expand \left(x^{2}y^{2}\right)^{-1}.

$$\frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}\left(x^{2}\right)^{-1}\left(y^{2}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}x^{-2}\left(y^{2}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}x^{-2}y^{-2}$$

Express \frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}x^{-2} as a single fraction.

$$\frac{\left(y^{11}\right)^{-2}x^{-2}}{\left(8x^{5}\right)^{-2}}y^{-2}$$

Express \frac{\left(y^{11}\right)^{-2}x^{-2}}{\left(8x^{5}\right)^{-2}}y^{-2} as a single fraction.

$$\frac{\left(y^{11}\right)^{-2}x^{-2}y^{-2}}{\left(8x^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and -2 to get -22.

$$\frac{y^{-22}x^{-2}y^{-2}}{\left(8x^{5}\right)^{-2}}$$

To multiply powers of the same base, add their exponents. Add -22 and -2 to get -24.

$$\frac{y^{-24}x^{-2}}{\left(8x^{5}\right)^{-2}}$$

Expand \left(8x^{5}\right)^{-2}.

$$\frac{y^{-24}x^{-2}}{8^{-2}\left(x^{5}\right)^{-2}}$$

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

$$\frac{y^{-24}x^{-2}}{8^{-2}x^{-10}}$$

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

$$\frac{y^{-24}x^{-2}}{\frac{1}{64}x^{-10}}$$

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

$$\frac{y^{-24}x^{8}}{\frac{1}{64}}$$

Divide y^{-24}x^{8} by \frac{1}{64} by multiplying y^{-24}x^{8} by the reciprocal of \frac{1}{64}.

$$y^{-24}x^{8}\times 64$$

Expand

$$\frac{64x^{8}}{y^{24}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

$$\left(\frac{x^{-4}y^{11}}{8x}\right)^{-2}\left(x^{2}y^{2}\right)^{-1}$$

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

$$\left(\frac{y^{11}}{8x^{5}}\right)^{-2}\left(x^{2}y^{2}\right)^{-1}$$

To raise \frac{y^{11}}{8x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}\left(x^{2}y^{2}\right)^{-1}$$

Expand \left(x^{2}y^{2}\right)^{-1}.

$$\frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}\left(x^{2}\right)^{-1}\left(y^{2}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}x^{-2}\left(y^{2}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}x^{-2}y^{-2}$$

Express \frac{\left(y^{11}\right)^{-2}}{\left(8x^{5}\right)^{-2}}x^{-2} as a single fraction.

$$\frac{\left(y^{11}\right)^{-2}x^{-2}}{\left(8x^{5}\right)^{-2}}y^{-2}$$

Express \frac{\left(y^{11}\right)^{-2}x^{-2}}{\left(8x^{5}\right)^{-2}}y^{-2} as a single fraction.

$$\frac{\left(y^{11}\right)^{-2}x^{-2}y^{-2}}{\left(8x^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and -2 to get -22.

$$\frac{y^{-22}x^{-2}y^{-2}}{\left(8x^{5}\right)^{-2}}$$

To multiply powers of the same base, add their exponents. Add -22 and -2 to get -24.

$$\frac{y^{-24}x^{-2}}{\left(8x^{5}\right)^{-2}}$$

Expand \left(8x^{5}\right)^{-2}.

$$\frac{y^{-24}x^{-2}}{8^{-2}\left(x^{5}\right)^{-2}}$$

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

$$\frac{y^{-24}x^{-2}}{8^{-2}x^{-10}}$$

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

$$\frac{y^{-24}x^{-2}}{\frac{1}{64}x^{-10}}$$

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

$$\frac{y^{-24}x^{8}}{\frac{1}{64}}$$

Divide y^{-24}x^{8} by \frac{1}{64} by multiplying y^{-24}x^{8} by the reciprocal of \frac{1}{64}.

$$y^{-24}x^{8}\times 64$$