Solve 4x(5x^frac{1{2}})^2

$$4 x ( 5 x ^ { \frac { 1 } { 2 } } ) ^ { 2 }$$

Evaluate

$$100x^{2}$$

Solution Steps

Expand \left(5x^{\frac{1}{2}}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

$$4x\times 5^{2}x^{1}$$

Calculate 5 to the power of 2 and get 25.

$$4x\times 25x^{1}$$

Calculate x to the power of 1 and get x.

$$4x\times 25x$$

Multiply 4 and 25 to get 100.

$$100xx$$

Multiply x and x to get x^{2}.

$$100x^{2}$$

Expand

$$100x^{2}$$

Solution Steps

Expand \left(5x^{\frac{1}{2}}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

$$4x\times 5^{2}x^{1}$$

Calculate 5 to the power of 2 and get 25.

$$4x\times 25x^{1}$$

Calculate x to the power of 1 and get x.

$$4x\times 25x$$

Multiply 4 and 25 to get 100.

$$100xx$$

Multiply x and x to get x^{2}.

$$100x^{2}$$