Solve 2x^3/(2y*2x^2y^3)^2

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

Evaluate

$$\frac{1}{8xy^{8}}$$

Solution Steps

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

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

Multiply 2 and 2 to get 4.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

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

Calculate 4 to the power of 2 and get 16.

$$\frac{2x^{3}}{16y^{8}x^{4}}$$

Cancel out 2x^{3} in both numerator and denominator.

$$\frac{1}{8xy^{8}}$$

Expand

$$\frac{1}{8xy^{8}}$$

Solution Steps

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

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

Multiply 2 and 2 to get 4.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

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

Calculate 4 to the power of 2 and get 16.

$$\frac{2x^{3}}{16y^{8}x^{4}}$$

Cancel out 2x^{3} in both numerator and denominator.

$$\frac{1}{8xy^{8}}$$