Solve 3x^3y^4*6xy^-5/(3xy)^2

$$\frac { 3 x ^ { 3 } y ^ { 4 } \cdot 6 x y ^ { - 5 } } { ( 3 x y ) ^ { 2 } }$$

Evaluate

$$\frac{2x^{2}}{y^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{3x^{4}y^{4}\times 6y^{-5}}{\left(3xy\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and -5 to get -1.

$$\frac{3x^{4}y^{-1}\times 6}{\left(3xy\right)^{2}}$$

Multiply 3 and 6 to get 18.

$$\frac{18x^{4}y^{-1}}{\left(3xy\right)^{2}}$$

Expand \left(3xy\right)^{2}.

$$\frac{18x^{4}y^{-1}}{3^{2}x^{2}y^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{18x^{4}y^{-1}}{9x^{2}y^{2}}$$

Cancel out 9x^{2} in both numerator and denominator.

$$\frac{2\times \frac{1}{y}x^{2}}{y^{2}}$$

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

$$\frac{2x^{2}}{y^{3}}$$

Expand

$$\frac{2x^{2}}{y^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{3x^{4}y^{4}\times 6y^{-5}}{\left(3xy\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and -5 to get -1.

$$\frac{3x^{4}y^{-1}\times 6}{\left(3xy\right)^{2}}$$

Multiply 3 and 6 to get 18.

$$\frac{18x^{4}y^{-1}}{\left(3xy\right)^{2}}$$

Expand \left(3xy\right)^{2}.

$$\frac{18x^{4}y^{-1}}{3^{2}x^{2}y^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{18x^{4}y^{-1}}{9x^{2}y^{2}}$$

Cancel out 9x^{2} in both numerator and denominator.

$$\frac{2\times \frac{1}{y}x^{2}}{y^{2}}$$

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

$$\frac{2x^{2}}{y^{3}}$$