Solve (frac{4x^{2}y^{2}}{3x^{-2}})^{-2}*(x^-2/x^-4y^5)^2

$$( \frac { 4 x ^ { 2 } y ^ { 2 } } { 3 x ^ { - 2 } } ) ^ { - 2 } \cdot ( \frac { x ^ { - 2 } } { x ^ { - 4 } y ^ { 5 } } ) ^ { 2 }$$

Evaluate

$$\frac{9}{16x^{4}y^{14}}$$

Solution Steps

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

$$\left(\frac{4y^{2}x^{4}}{3}\right)^{-2}\times \left(\frac{x^{-2}}{x^{-4}y^{5}}\right)^{2}$$

To raise \frac{4y^{2}x^{4}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4y^{2}x^{4}\right)^{-2}}{3^{-2}}\times \left(\frac{x^{-2}}{x^{-4}y^{5}}\right)^{2}$$

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

$$\frac{\left(4y^{2}x^{4}\right)^{-2}}{3^{-2}}\times \left(\frac{x^{2}}{y^{5}}\right)^{2}$$

To raise \frac{x^{2}}{y^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4y^{2}x^{4}\right)^{-2}}{3^{-2}}\times \frac{\left(x^{2}\right)^{2}}{\left(y^{5}\right)^{2}}$$

Multiply \frac{\left(4y^{2}x^{4}\right)^{-2}}{3^{-2}} times \frac{\left(x^{2}\right)^{2}}{\left(y^{5}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4y^{2}x^{4}\right)^{-2}\left(x^{2}\right)^{2}}{3^{-2}\left(y^{5}\right)^{2}}$$

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

$$\frac{\left(4y^{2}x^{4}\right)^{-2}x^{4}}{3^{-2}\left(y^{5}\right)^{2}}$$

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

$$\frac{\left(4y^{2}x^{4}\right)^{-2}x^{4}}{3^{-2}y^{10}}$$

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

$$\frac{4^{-2}\left(y^{2}\right)^{-2}\left(x^{4}\right)^{-2}x^{4}}{3^{-2}y^{10}}$$

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

$$\frac{4^{-2}y^{-4}\left(x^{4}\right)^{-2}x^{4}}{3^{-2}y^{10}}$$

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

$$\frac{4^{-2}y^{-4}x^{-8}x^{4}}{3^{-2}y^{10}}$$

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

$$\frac{\frac{1}{16}y^{-4}x^{-8}x^{4}}{3^{-2}y^{10}}$$

To multiply powers of the same base, add their exponents. Add -8 and 4 to get -4.

$$\frac{\frac{1}{16}y^{-4}x^{-4}}{3^{-2}y^{10}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{16}y^{-4}x^{-4}}{\frac{1}{9}y^{10}}$$

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

$$\frac{\frac{1}{16}x^{-4}}{\frac{1}{9}y^{14}}$$

Expand

$$\frac{9}{16x^{4}y^{14}}$$

Solution Steps

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

$$\left(\frac{4y^{2}x^{4}}{3}\right)^{-2}\times \left(\frac{x^{-2}}{x^{-4}y^{5}}\right)^{2}$$

To raise \frac{4y^{2}x^{4}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4y^{2}x^{4}\right)^{-2}}{3^{-2}}\times \left(\frac{x^{-2}}{x^{-4}y^{5}}\right)^{2}$$

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

$$\frac{\left(4y^{2}x^{4}\right)^{-2}}{3^{-2}}\times \left(\frac{x^{2}}{y^{5}}\right)^{2}$$

To raise \frac{x^{2}}{y^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4y^{2}x^{4}\right)^{-2}}{3^{-2}}\times \frac{\left(x^{2}\right)^{2}}{\left(y^{5}\right)^{2}}$$

Multiply \frac{\left(4y^{2}x^{4}\right)^{-2}}{3^{-2}} times \frac{\left(x^{2}\right)^{2}}{\left(y^{5}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4y^{2}x^{4}\right)^{-2}\left(x^{2}\right)^{2}}{3^{-2}\left(y^{5}\right)^{2}}$$

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

$$\frac{\left(4y^{2}x^{4}\right)^{-2}x^{4}}{3^{-2}\left(y^{5}\right)^{2}}$$

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

$$\frac{\left(4y^{2}x^{4}\right)^{-2}x^{4}}{3^{-2}y^{10}}$$

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

$$\frac{4^{-2}\left(y^{2}\right)^{-2}\left(x^{4}\right)^{-2}x^{4}}{3^{-2}y^{10}}$$

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

$$\frac{4^{-2}y^{-4}\left(x^{4}\right)^{-2}x^{4}}{3^{-2}y^{10}}$$

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

$$\frac{4^{-2}y^{-4}x^{-8}x^{4}}{3^{-2}y^{10}}$$

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

$$\frac{\frac{1}{16}y^{-4}x^{-8}x^{4}}{3^{-2}y^{10}}$$

To multiply powers of the same base, add their exponents. Add -8 and 4 to get -4.

$$\frac{\frac{1}{16}y^{-4}x^{-4}}{3^{-2}y^{10}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{16}y^{-4}x^{-4}}{\frac{1}{9}y^{10}}$$

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

$$\frac{\frac{1}{16}x^{-4}}{\frac{1}{9}y^{14}}$$