Solve left(3x^-4y^-7right)^2/{left(2x^-3{y^-2right)}^-4}

$$\frac{ { \left(3 { x }^{ -4 } { y }^{ -7 } \right) }^{ 2 } }{ { \left(2 { x }^{ -3 } { y }^{ -2 } \right) }^{ -4 } }$$

Evaluate

$$\frac{144}{x^{20}y^{22}}$$

Solution Steps

Expand \left(3x^{-4}y^{-7}\right)^{2}.

$$\frac{3^{2}\left(x^{-4}\right)^{2}\left(y^{-7}\right)^{2}}{\left(2x^{-3}y^{-2}\right)^{-4}}$$

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

$$\frac{3^{2}x^{-8}\left(y^{-7}\right)^{2}}{\left(2x^{-3}y^{-2}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply -7 and 2 to get -14.

$$\frac{3^{2}x^{-8}y^{-14}}{\left(2x^{-3}y^{-2}\right)^{-4}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{-8}y^{-14}}{\left(2x^{-3}y^{-2}\right)^{-4}}$$

Expand \left(2x^{-3}y^{-2}\right)^{-4}.

$$\frac{9x^{-8}y^{-14}}{2^{-4}\left(x^{-3}\right)^{-4}\left(y^{-2}\right)^{-4}}$$

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

$$\frac{9x^{-8}y^{-14}}{2^{-4}x^{12}\left(y^{-2}\right)^{-4}}$$

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

$$\frac{9x^{-8}y^{-14}}{2^{-4}x^{12}y^{8}}$$

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

$$\frac{9x^{-8}y^{-14}}{\frac{1}{16}x^{12}y^{8}}$$

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

$$\frac{9}{\frac{1}{16}x^{20}y^{22}}$$

Expand

$$\frac{144}{x^{20}y^{22}}$$

Solution Steps

Expand \left(3x^{-4}y^{-7}\right)^{2}.

$$\frac{3^{2}\left(x^{-4}\right)^{2}\left(y^{-7}\right)^{2}}{\left(2x^{-3}y^{-2}\right)^{-4}}$$

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

$$\frac{3^{2}x^{-8}\left(y^{-7}\right)^{2}}{\left(2x^{-3}y^{-2}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply -7 and 2 to get -14.

$$\frac{3^{2}x^{-8}y^{-14}}{\left(2x^{-3}y^{-2}\right)^{-4}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{-8}y^{-14}}{\left(2x^{-3}y^{-2}\right)^{-4}}$$

Expand \left(2x^{-3}y^{-2}\right)^{-4}.

$$\frac{9x^{-8}y^{-14}}{2^{-4}\left(x^{-3}\right)^{-4}\left(y^{-2}\right)^{-4}}$$

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

$$\frac{9x^{-8}y^{-14}}{2^{-4}x^{12}\left(y^{-2}\right)^{-4}}$$

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

$$\frac{9x^{-8}y^{-14}}{2^{-4}x^{12}y^{8}}$$

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

$$\frac{9x^{-8}y^{-14}}{\frac{1}{16}x^{12}y^{8}}$$

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

$$\frac{9}{\frac{1}{16}x^{20}y^{22}}$$