Solve frac{(12x^{4}y^-3)^2}{2x^4y^-3}

$$\frac { ( 12 x ^ { 4 } y ^ { - 3 } ) ^ { 2 } } { 2 x ^ { 4 } y ^ { - 3 } }$$

Evaluate

$$\frac{72x^{4}}{y^{3}}$$

Solution Steps

Expand \left(12x^{4}y^{-3}\right)^{2}.

$$\frac{12^{2}\left(x^{4}\right)^{2}\left(y^{-3}\right)^{2}}{2x^{4}y^{-3}}$$

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

$$\frac{12^{2}x^{8}\left(y^{-3}\right)^{2}}{2x^{4}y^{-3}}$$

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

$$\frac{12^{2}x^{8}y^{-6}}{2x^{4}y^{-3}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{144x^{8}y^{-6}}{2x^{4}y^{-3}}$$

Cancel out 2x^{4} in both numerator and denominator.

$$\frac{72y^{-6}x^{4}}{y^{-3}}$$

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

$$\frac{72x^{4}}{y^{3}}$$

Expand

$$\frac{72x^{4}}{y^{3}}$$

Solution Steps

Expand \left(12x^{4}y^{-3}\right)^{2}.

$$\frac{12^{2}\left(x^{4}\right)^{2}\left(y^{-3}\right)^{2}}{2x^{4}y^{-3}}$$

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

$$\frac{12^{2}x^{8}\left(y^{-3}\right)^{2}}{2x^{4}y^{-3}}$$

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

$$\frac{12^{2}x^{8}y^{-6}}{2x^{4}y^{-3}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{144x^{8}y^{-6}}{2x^{4}y^{-3}}$$

Cancel out 2x^{4} in both numerator and denominator.

$$\frac{72y^{-6}x^{4}}{y^{-3}}$$

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

$$\frac{72x^{4}}{y^{3}}$$