Solve {left(x2)2((xx^2(5)sqrt{x^2/}right)}^2

$${ \left(x2)2((x { x }^{ 2 } (5) \sqrt{ \frac{ { x }^{ 2 } }{ } } \right) }^{ 2 }$$

Evaluate

$$50x_{2}x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2x_{2}\left(x^{3}\times 5\sqrt{\frac{x^{2}}{1}}\right)^{2}$$

Anything divided by one gives itself.

$$2x_{2}\left(x^{3}\times 5\sqrt{x^{2}}\right)^{2}$$

Expand \left(x^{3}\times 5\sqrt{x^{2}}\right)^{2}.

$$2x_{2}\left(x^{3}\right)^{2}\times 5^{2}\left(\sqrt{x^{2}}\right)^{2}$$

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

$$2x_{2}x^{6}\times 5^{2}\left(\sqrt{x^{2}}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$2x_{2}x^{6}\times 25\left(\sqrt{x^{2}}\right)^{2}$$

Calculate \sqrt{x^{2}} to the power of 2 and get x^{2}.

$$2x_{2}x^{6}\times 25x^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$2x_{2}x^{8}\times 25$$

Multiply 2 and 25 to get 50.

$$50x_{2}x^{8}$$

Expand

$$50x_{2}x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2x_{2}\left(x^{3}\times 5\sqrt{\frac{x^{2}}{1}}\right)^{2}$$

Anything divided by one gives itself.

$$2x_{2}\left(x^{3}\times 5\sqrt{x^{2}}\right)^{2}$$

Expand \left(x^{3}\times 5\sqrt{x^{2}}\right)^{2}.

$$2x_{2}\left(x^{3}\right)^{2}\times 5^{2}\left(\sqrt{x^{2}}\right)^{2}$$

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

$$2x_{2}x^{6}\times 5^{2}\left(\sqrt{x^{2}}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$2x_{2}x^{6}\times 25\left(\sqrt{x^{2}}\right)^{2}$$

Calculate \sqrt{x^{2}} to the power of 2 and get x^{2}.

$$2x_{2}x^{6}\times 25x^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$2x_{2}x^{8}\times 25$$

Multiply 2 and 25 to get 50.

$$50x_{2}x^{8}$$