Solve (3x^6y)*(-4xy^2)^2div(0.5x^2y)

$$( 3 x ^ { 6 } y ) \cdot ( - 4 x y ^ { 2 } ) ^ { 2 } \div ( 0.5 x ^ { 2 } y )$$

Evaluate

$$96y^{4}x^{6}$$

Solution Steps

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

$$\frac{3x^{4}\left(-4xy^{2}\right)^{2}}{0.5}$$

Expand \left(-4xy^{2}\right)^{2}.

$$\frac{3x^{4}\left(-4\right)^{2}x^{2}\left(y^{2}\right)^{2}}{0.5}$$

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

$$\frac{3x^{4}\left(-4\right)^{2}x^{2}y^{4}}{0.5}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{3x^{4}\times 16x^{2}y^{4}}{0.5}$$

Multiply 3 and 16 to get 48.

$$\frac{48x^{4}x^{2}y^{4}}{0.5}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{48x^{6}y^{4}}{0.5}$$

Divide 48x^{6}y^{4} by 0.5 to get 96x^{6}y^{4}.

$$96x^{6}y^{4}$$

Expand

$$96y^{4}x^{6}$$

Solution Steps

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

$$\frac{3x^{4}\left(-4xy^{2}\right)^{2}}{0.5}$$

Expand \left(-4xy^{2}\right)^{2}.

$$\frac{3x^{4}\left(-4\right)^{2}x^{2}\left(y^{2}\right)^{2}}{0.5}$$

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

$$\frac{3x^{4}\left(-4\right)^{2}x^{2}y^{4}}{0.5}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{3x^{4}\times 16x^{2}y^{4}}{0.5}$$

Multiply 3 and 16 to get 48.

$$\frac{48x^{4}x^{2}y^{4}}{0.5}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{48x^{6}y^{4}}{0.5}$$

Divide 48x^{6}y^{4} by 0.5 to get 96x^{6}y^{4}.

$$96x^{6}y^{4}$$