Solve [frac{(72x^{-3}y^{-2})*(24^{-1}x^{-3})^{2}}{(48x^-5y^4)^-3}]^2

$$[ \frac { ( 72 x ^ { - 3 } y ^ { - 2 } ) \cdot ( 24 ^ { - 1 } x ^ { - 3 } ) ^ { 2 } } { ( 48 x ^ { - 5 } y ^ { 4 } ) ^ { - 3 } } ] ^ { 2 }$$

Evaluate

$$\frac{191102976y^{20}}{x^{48}}$$

Solution Steps

Calculate 24 to the power of -1 and get \frac{1}{24}.

$$\left(\frac{72x^{-3}y^{-2}\times \left(\frac{1}{24}x^{-3}\right)^{2}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

Expand \left(\frac{1}{24}x^{-3}\right)^{2}.

$$\left(\frac{72x^{-3}y^{-2}\times \left(\frac{1}{24}\right)^{2}\left(x^{-3}\right)^{2}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

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

$$\left(\frac{72x^{-3}y^{-2}\times \left(\frac{1}{24}\right)^{2}x^{-6}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

Calculate \frac{1}{24} to the power of 2 and get \frac{1}{576}.

$$\left(\frac{72x^{-3}y^{-2}\times \frac{1}{576}x^{-6}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

Multiply 72 and \frac{1}{576} to get \frac{1}{8}.

$$\left(\frac{\frac{1}{8}x^{-3}y^{-2}x^{-6}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add -3 and -6 to get -9.

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

Expand \left(48x^{-5}y^{4}\right)^{-3}.

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{48^{-3}\left(x^{-5}\right)^{-3}\left(y^{4}\right)^{-3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{48^{-3}x^{15}\left(y^{4}\right)^{-3}}\right)^{2}$$

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

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{48^{-3}x^{15}y^{-12}}\right)^{2}$$

Calculate 48 to the power of -3 and get \frac{1}{110592}.

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{\frac{1}{110592}x^{15}y^{-12}}\right)^{2}$$

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

$$\left(\frac{\frac{1}{8}x^{-9}y^{10}}{\frac{1}{110592}x^{15}}\right)^{2}$$

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

$$\left(\frac{\frac{1}{8}y^{10}}{\frac{1}{110592}x^{24}}\right)^{2}$$

To raise \frac{\frac{1}{8}y^{10}}{\frac{1}{110592}x^{24}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\frac{1}{8}y^{10}\right)^{2}}{\left(\frac{1}{110592}x^{24}\right)^{2}}$$

Expand \left(\frac{1}{8}y^{10}\right)^{2}.

$$\frac{\left(\frac{1}{8}\right)^{2}\left(y^{10}\right)^{2}}{\left(\frac{1}{110592}x^{24}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$\frac{\left(\frac{1}{8}\right)^{2}y^{20}}{\left(\frac{1}{110592}x^{24}\right)^{2}}$$

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

$$\frac{\frac{1}{64}y^{20}}{\left(\frac{1}{110592}x^{24}\right)^{2}}$$

Expand \left(\frac{1}{110592}x^{24}\right)^{2}.

$$\frac{\frac{1}{64}y^{20}}{\left(\frac{1}{110592}\right)^{2}\left(x^{24}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 24 and 2 to get 48.

$$\frac{\frac{1}{64}y^{20}}{\left(\frac{1}{110592}\right)^{2}x^{48}}$$

Calculate \frac{1}{110592} to the power of 2 and get \frac{1}{12230590464}.

$$\frac{\frac{1}{64}y^{20}}{\frac{1}{12230590464}x^{48}}$$

Expand

$$\frac{191102976y^{20}}{x^{48}}$$

Solution Steps

Calculate 24 to the power of -1 and get \frac{1}{24}.

$$\left(\frac{72x^{-3}y^{-2}\times \left(\frac{1}{24}x^{-3}\right)^{2}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

Expand \left(\frac{1}{24}x^{-3}\right)^{2}.

$$\left(\frac{72x^{-3}y^{-2}\times \left(\frac{1}{24}\right)^{2}\left(x^{-3}\right)^{2}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

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

$$\left(\frac{72x^{-3}y^{-2}\times \left(\frac{1}{24}\right)^{2}x^{-6}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

Calculate \frac{1}{24} to the power of 2 and get \frac{1}{576}.

$$\left(\frac{72x^{-3}y^{-2}\times \frac{1}{576}x^{-6}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

Multiply 72 and \frac{1}{576} to get \frac{1}{8}.

$$\left(\frac{\frac{1}{8}x^{-3}y^{-2}x^{-6}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add -3 and -6 to get -9.

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{\left(48x^{-5}y^{4}\right)^{-3}}\right)^{2}$$

Expand \left(48x^{-5}y^{4}\right)^{-3}.

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{48^{-3}\left(x^{-5}\right)^{-3}\left(y^{4}\right)^{-3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{48^{-3}x^{15}\left(y^{4}\right)^{-3}}\right)^{2}$$

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

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{48^{-3}x^{15}y^{-12}}\right)^{2}$$

Calculate 48 to the power of -3 and get \frac{1}{110592}.

$$\left(\frac{\frac{1}{8}x^{-9}y^{-2}}{\frac{1}{110592}x^{15}y^{-12}}\right)^{2}$$

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

$$\left(\frac{\frac{1}{8}x^{-9}y^{10}}{\frac{1}{110592}x^{15}}\right)^{2}$$

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

$$\left(\frac{\frac{1}{8}y^{10}}{\frac{1}{110592}x^{24}}\right)^{2}$$

To raise \frac{\frac{1}{8}y^{10}}{\frac{1}{110592}x^{24}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\frac{1}{8}y^{10}\right)^{2}}{\left(\frac{1}{110592}x^{24}\right)^{2}}$$

Expand \left(\frac{1}{8}y^{10}\right)^{2}.

$$\frac{\left(\frac{1}{8}\right)^{2}\left(y^{10}\right)^{2}}{\left(\frac{1}{110592}x^{24}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$\frac{\left(\frac{1}{8}\right)^{2}y^{20}}{\left(\frac{1}{110592}x^{24}\right)^{2}}$$

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

$$\frac{\frac{1}{64}y^{20}}{\left(\frac{1}{110592}x^{24}\right)^{2}}$$

Expand \left(\frac{1}{110592}x^{24}\right)^{2}.

$$\frac{\frac{1}{64}y^{20}}{\left(\frac{1}{110592}\right)^{2}\left(x^{24}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 24 and 2 to get 48.

$$\frac{\frac{1}{64}y^{20}}{\left(\frac{1}{110592}\right)^{2}x^{48}}$$

Calculate \frac{1}{110592} to the power of 2 and get \frac{1}{12230590464}.

$$\frac{\frac{1}{64}y^{20}}{\frac{1}{12230590464}x^{48}}$$