Solve frac{2^{5}*x^{4}*y^3*y^2}{4*(2x)^3*y^4}

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

Evaluate

$$xy$$

Solution Steps

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

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

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

$$\frac{2^{5}yx^{4}}{4\times \left(2x\right)^{3}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32yx^{4}}{4\times \left(2x\right)^{3}}$$

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

$$\frac{32yx^{4}}{4\times 2^{3}x^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{32yx^{4}}{4\times 8x^{3}}$$

Multiply 4 and 8 to get 32.

$$\frac{32yx^{4}}{32x^{3}}$$

Cancel out 32x^{3} in both numerator and denominator.

$$xy$$

Expand

$$xy$$

Solution Steps

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

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

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

$$\frac{2^{5}yx^{4}}{4\times \left(2x\right)^{3}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32yx^{4}}{4\times \left(2x\right)^{3}}$$

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

$$\frac{32yx^{4}}{4\times 2^{3}x^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{32yx^{4}}{4\times 8x^{3}}$$

Multiply 4 and 8 to get 32.

$$\frac{32yx^{4}}{32x^{3}}$$

Cancel out 32x^{3} in both numerator and denominator.

$$xy$$