Solve left(12x^3y^-3right)^4/{left(19x^4{y^4right)}^3}

$$\frac{ { \left(12 { x }^{ 3 } { y }^{ -3 } \right) }^{ 4 } }{ { \left(19 { x }^{ 4 } { y }^{ 4 } \right) }^{ 3 } }$$

Evaluate

$$\frac{20736}{6859y^{24}}$$

Solution Steps

Expand \left(12x^{3}y^{-3}\right)^{4}.

$$\frac{12^{4}\left(x^{3}\right)^{4}\left(y^{-3}\right)^{4}}{\left(19x^{4}y^{4}\right)^{3}}$$

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

$$\frac{12^{4}x^{12}\left(y^{-3}\right)^{4}}{\left(19x^{4}y^{4}\right)^{3}}$$

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

$$\frac{12^{4}x^{12}y^{-12}}{\left(19x^{4}y^{4}\right)^{3}}$$

Calculate 12 to the power of 4 and get 20736.

$$\frac{20736x^{12}y^{-12}}{\left(19x^{4}y^{4}\right)^{3}}$$

Expand \left(19x^{4}y^{4}\right)^{3}.

$$\frac{20736x^{12}y^{-12}}{19^{3}\left(x^{4}\right)^{3}\left(y^{4}\right)^{3}}$$

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

$$\frac{20736x^{12}y^{-12}}{19^{3}x^{12}\left(y^{4}\right)^{3}}$$

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

$$\frac{20736x^{12}y^{-12}}{19^{3}x^{12}y^{12}}$$

Calculate 19 to the power of 3 and get 6859.

$$\frac{20736x^{12}y^{-12}}{6859x^{12}y^{12}}$$

Cancel out x^{12} in both numerator and denominator.

$$\frac{20736y^{-12}}{6859y^{12}}$$

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

$$\frac{20736}{6859y^{24}}$$

Expand

$$\frac{20736}{6859y^{24}}$$

Solution Steps

Expand \left(12x^{3}y^{-3}\right)^{4}.

$$\frac{12^{4}\left(x^{3}\right)^{4}\left(y^{-3}\right)^{4}}{\left(19x^{4}y^{4}\right)^{3}}$$

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

$$\frac{12^{4}x^{12}\left(y^{-3}\right)^{4}}{\left(19x^{4}y^{4}\right)^{3}}$$

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

$$\frac{12^{4}x^{12}y^{-12}}{\left(19x^{4}y^{4}\right)^{3}}$$

Calculate 12 to the power of 4 and get 20736.

$$\frac{20736x^{12}y^{-12}}{\left(19x^{4}y^{4}\right)^{3}}$$

Expand \left(19x^{4}y^{4}\right)^{3}.

$$\frac{20736x^{12}y^{-12}}{19^{3}\left(x^{4}\right)^{3}\left(y^{4}\right)^{3}}$$

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

$$\frac{20736x^{12}y^{-12}}{19^{3}x^{12}\left(y^{4}\right)^{3}}$$

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

$$\frac{20736x^{12}y^{-12}}{19^{3}x^{12}y^{12}}$$

Calculate 19 to the power of 3 and get 6859.

$$\frac{20736x^{12}y^{-12}}{6859x^{12}y^{12}}$$

Cancel out x^{12} in both numerator and denominator.

$$\frac{20736y^{-12}}{6859y^{12}}$$

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

$$\frac{20736}{6859y^{24}}$$