Solve frac{((2x^{3}y^{2}*2x^{2}y^{2})^{0}*y^3)^4}{2x^2y^-1}

$$\frac { ( ( 2 x ^ { 3 } y ^ { 2 } \cdot 2 x ^ { 2 } y ^ { 2 } ) ^ { 0 } \cdot y ^ { 3 } ) ^ { 4 } } { 2 x ^ { 2 } y ^ { - 1 } }$$

Evaluate

$$\frac{y^{13}}{2x^{2}}$$

Solution Steps

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

$$\frac{\left(\left(2x^{5}y^{2}\times 2y^{2}\right)^{0}y^{3}\right)^{4}}{2x^{2}y^{-1}}$$

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

$$\frac{\left(\left(2x^{5}y^{4}\times 2\right)^{0}y^{3}\right)^{4}}{2x^{2}y^{-1}}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(\left(4x^{5}y^{4}\right)^{0}y^{3}\right)^{4}}{2x^{2}y^{-1}}$$

Calculate 4x^{5}y^{4} to the power of 0 and get 1.

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

Expand \left(1y^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{1^{4}y^{12}}{2x^{2}y^{-1}}$$

Calculate 1 to the power of 4 and get 1.

$$\frac{1y^{12}}{2x^{2}y^{-1}}$$

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

$$\frac{y^{13}}{2x^{2}}$$

Expand

$$\frac{y^{13}}{2x^{2}}$$

Solution Steps

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

$$\frac{\left(\left(2x^{5}y^{2}\times 2y^{2}\right)^{0}y^{3}\right)^{4}}{2x^{2}y^{-1}}$$

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

$$\frac{\left(\left(2x^{5}y^{4}\times 2\right)^{0}y^{3}\right)^{4}}{2x^{2}y^{-1}}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(\left(4x^{5}y^{4}\right)^{0}y^{3}\right)^{4}}{2x^{2}y^{-1}}$$

Calculate 4x^{5}y^{4} to the power of 0 and get 1.

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

Expand \left(1y^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{1^{4}y^{12}}{2x^{2}y^{-1}}$$

Calculate 1 to the power of 4 and get 1.

$$\frac{1y^{12}}{2x^{2}y^{-1}}$$

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

$$\frac{y^{13}}{2x^{2}}$$