Solve (2x^frac{1{3}}y^2)^7

$$( 2 x ^ { \frac { 1 } { 3 } } y ^ { 2 } ) ^ { 7 }$$

Evaluate

$$128x^{\frac{7}{3}}y^{14}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2\sqrt[3]{x}y^{2}\right)^{7}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$2^{7}\left(\sqrt[3]{x}\right)^{7}\left(y^{2}\right)^{7}$$

Raise 2 to the power 7.

$$128\left(\sqrt[3]{x}\right)^{7}\left(y^{2}\right)^{7}$$

To raise a power to another power, multiply the exponents.

$$128x^{\frac{1}{3}\times 7}y^{2\times 7}$$

Multiply \frac{1}{3} times 7.

$$128x^{\frac{7}{3}}y^{2\times 7}$$

Multiply 2 times 7.

$$128x^{\frac{7}{3}}y^{14}$$

Expand

$$128x^{\frac{7}{3}}y^{14}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2\sqrt[3]{x}y^{2}\right)^{7}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$2^{7}\left(\sqrt[3]{x}\right)^{7}\left(y^{2}\right)^{7}$$

Raise 2 to the power 7.

$$128\left(\sqrt[3]{x}\right)^{7}\left(y^{2}\right)^{7}$$

To raise a power to another power, multiply the exponents.

$$128x^{\frac{1}{3}\times 7}y^{2\times 7}$$

Multiply \frac{1}{3} times 7.

$$128x^{\frac{7}{3}}y^{2\times 7}$$

Multiply 2 times 7.

$$128x^{\frac{7}{3}}y^{14}$$