Solve frac{4xy^{2}*8x^3y^3}{(4xy^2)^2}

$$\frac { 4 x y ^ { 2 } \cdot 8 x ^ { 3 } y ^ { 3 } } { ( 4 x y ^ { 2 } ) ^ { 2 } }$$

Evaluate

$$2yx^{2}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{4x^{4}y^{5}\times 8}{\left(4xy^{2}\right)^{2}}$$

Multiply 4 and 8 to get 32.

$$\frac{32x^{4}y^{5}}{\left(4xy^{2}\right)^{2}}$$

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

$$\frac{32x^{4}y^{5}}{4^{2}x^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{32x^{4}y^{5}}{4^{2}x^{2}y^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{32x^{4}y^{5}}{16x^{2}y^{4}}$$

Cancel out 16x^{2}y^{4} in both numerator and denominator.

$$2yx^{2}$$

Expand

$$2yx^{2}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{4x^{4}y^{5}\times 8}{\left(4xy^{2}\right)^{2}}$$

Multiply 4 and 8 to get 32.

$$\frac{32x^{4}y^{5}}{\left(4xy^{2}\right)^{2}}$$

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

$$\frac{32x^{4}y^{5}}{4^{2}x^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{32x^{4}y^{5}}{4^{2}x^{2}y^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{32x^{4}y^{5}}{16x^{2}y^{4}}$$

Cancel out 16x^{2}y^{4} in both numerator and denominator.

$$2yx^{2}$$