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

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

Evaluate

$$2y^{10}x^{11}$$

Solution Steps

To raise \frac{x^{4}}{2y^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(x^{4}\right)^{2}}{\left(2y^{-2}\right)^{2}}\times 2^{3}x^{3}y^{6}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(x^{4}\right)^{2}}{\left(2y^{-2}\right)^{2}}\times 8x^{3}y^{6}$$

Express \frac{\left(x^{4}\right)^{2}}{\left(2y^{-2}\right)^{2}}\times 8 as a single fraction.

$$\frac{\left(x^{4}\right)^{2}\times 8}{\left(2y^{-2}\right)^{2}}x^{3}y^{6}$$

Express \frac{\left(x^{4}\right)^{2}\times 8}{\left(2y^{-2}\right)^{2}}x^{3} as a single fraction.

$$\frac{\left(x^{4}\right)^{2}\times 8x^{3}}{\left(2y^{-2}\right)^{2}}y^{6}$$

Express \frac{\left(x^{4}\right)^{2}\times 8x^{3}}{\left(2y^{-2}\right)^{2}}y^{6} as a single fraction.

$$\frac{\left(x^{4}\right)^{2}\times 8x^{3}y^{6}}{\left(2y^{-2}\right)^{2}}$$

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

$$\frac{x^{8}\times 8x^{3}y^{6}}{\left(2y^{-2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\frac{x^{11}\times 8y^{6}}{\left(2y^{-2}\right)^{2}}$$

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

$$\frac{x^{11}\times 8y^{6}}{2^{2}\left(y^{-2}\right)^{2}}$$

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

$$\frac{x^{11}\times 8y^{6}}{2^{2}y^{-4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{11}\times 8y^{6}}{4y^{-4}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2y^{6}x^{11}}{y^{-4}}$$

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

$$2y^{10}x^{11}$$

Expand

$$2y^{10}x^{11}$$

Solution Steps

To raise \frac{x^{4}}{2y^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(x^{4}\right)^{2}}{\left(2y^{-2}\right)^{2}}\times 2^{3}x^{3}y^{6}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(x^{4}\right)^{2}}{\left(2y^{-2}\right)^{2}}\times 8x^{3}y^{6}$$

Express \frac{\left(x^{4}\right)^{2}}{\left(2y^{-2}\right)^{2}}\times 8 as a single fraction.

$$\frac{\left(x^{4}\right)^{2}\times 8}{\left(2y^{-2}\right)^{2}}x^{3}y^{6}$$

Express \frac{\left(x^{4}\right)^{2}\times 8}{\left(2y^{-2}\right)^{2}}x^{3} as a single fraction.

$$\frac{\left(x^{4}\right)^{2}\times 8x^{3}}{\left(2y^{-2}\right)^{2}}y^{6}$$

Express \frac{\left(x^{4}\right)^{2}\times 8x^{3}}{\left(2y^{-2}\right)^{2}}y^{6} as a single fraction.

$$\frac{\left(x^{4}\right)^{2}\times 8x^{3}y^{6}}{\left(2y^{-2}\right)^{2}}$$

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

$$\frac{x^{8}\times 8x^{3}y^{6}}{\left(2y^{-2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\frac{x^{11}\times 8y^{6}}{\left(2y^{-2}\right)^{2}}$$

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

$$\frac{x^{11}\times 8y^{6}}{2^{2}\left(y^{-2}\right)^{2}}$$

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

$$\frac{x^{11}\times 8y^{6}}{2^{2}y^{-4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{11}\times 8y^{6}}{4y^{-4}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2y^{6}x^{11}}{y^{-4}}$$

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

$$2y^{10}x^{11}$$