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

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

Evaluate

$$\frac{4x^{10}}{81y^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

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

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

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

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

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

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

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

Calculate 3 to the power of 4 and get 81.

$$\frac{4x^{-2}y^{3}}{81x^{-12}y^{8}}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{4x^{-2}}{81x^{-12}y^{5}}$$

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

$$\frac{4x^{10}}{81y^{5}}$$

Expand

$$\frac{4x^{10}}{81y^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

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

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

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

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

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

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

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

Calculate 3 to the power of 4 and get 81.

$$\frac{4x^{-2}y^{3}}{81x^{-12}y^{8}}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{4x^{-2}}{81x^{-12}y^{5}}$$

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

$$\frac{4x^{10}}{81y^{5}}$$