Solve (2x^3y)^2div54y^2/xv

$$( 2 x ^ { 3 } y ) ^ { 2 } \div \frac { 54 y ^ { 2 } } { x } v$$

Evaluate

$$\frac{2vx^{7}}{27}$$

Solution Steps

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

$$\frac{2^{2}\left(x^{3}\right)^{2}y^{2}}{\frac{54y^{2}}{x}}v$$

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

$$\frac{2^{2}x^{6}y^{2}}{\frac{54y^{2}}{x}}v$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{6}y^{2}}{\frac{54y^{2}}{x}}v$$

Divide 4x^{6}y^{2} by \frac{54y^{2}}{x} by multiplying 4x^{6}y^{2} by the reciprocal of \frac{54y^{2}}{x}.

$$\frac{4x^{6}y^{2}x}{54y^{2}}v$$

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

$$\frac{2xx^{6}}{27}v$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{2x^{7}}{27}v$$

Express \frac{2x^{7}}{27}v as a single fraction.

$$\frac{2x^{7}v}{27}$$

Expand

$$\frac{2vx^{7}}{27}$$

Solution Steps

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

$$\frac{2^{2}\left(x^{3}\right)^{2}y^{2}}{\frac{54y^{2}}{x}}v$$

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

$$\frac{2^{2}x^{6}y^{2}}{\frac{54y^{2}}{x}}v$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{6}y^{2}}{\frac{54y^{2}}{x}}v$$

Divide 4x^{6}y^{2} by \frac{54y^{2}}{x} by multiplying 4x^{6}y^{2} by the reciprocal of \frac{54y^{2}}{x}.

$$\frac{4x^{6}y^{2}x}{54y^{2}}v$$

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

$$\frac{2xx^{6}}{27}v$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{2x^{7}}{27}v$$

Express \frac{2x^{7}}{27}v as a single fraction.

$$\frac{2x^{7}v}{27}$$