Solve {left(xsqrt{frac{x/289}}{8}right)}^2

$${ \left( \frac{ x \sqrt{ \frac{ x }{ 289 } } }{ 8 } \right) }^{ 2 }$$

Evaluate

$$\frac{x^{3}}{18496}$$

Solution Steps

To raise \frac{x\sqrt{\frac{x}{289}}}{8} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x\sqrt{\frac{x}{289}}\right)^{2}}{8^{2}}$$

Expand \left(x\sqrt{\frac{x}{289}}\right)^{2}.

$$\frac{x^{2}\left(\sqrt{\frac{x}{289}}\right)^{2}}{8^{2}}$$

Calculate \sqrt{\frac{x}{289}} to the power of 2 and get \frac{x}{289}.

$$\frac{x^{2}\times \frac{x}{289}}{8^{2}}$$

Express x^{2}\times \frac{x}{289} as a single fraction.

$$\frac{\frac{x^{2}x}{289}}{8^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\frac{x^{2}x}{289}}{64}$$

Express \frac{\frac{x^{2}x}{289}}{64} as a single fraction.

$$\frac{x^{2}x}{289\times 64}$$

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

$$\frac{x^{3}}{289\times 64}$$

Multiply 289 and 64 to get 18496.

$$\frac{x^{3}}{18496}$$

Expand

$$\frac{x^{3}}{18496}$$

Solution Steps

To raise \frac{x\sqrt{\frac{x}{289}}}{8} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x\sqrt{\frac{x}{289}}\right)^{2}}{8^{2}}$$

Expand \left(x\sqrt{\frac{x}{289}}\right)^{2}.

$$\frac{x^{2}\left(\sqrt{\frac{x}{289}}\right)^{2}}{8^{2}}$$

Calculate \sqrt{\frac{x}{289}} to the power of 2 and get \frac{x}{289}.

$$\frac{x^{2}\times \frac{x}{289}}{8^{2}}$$

Express x^{2}\times \frac{x}{289} as a single fraction.

$$\frac{\frac{x^{2}x}{289}}{8^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\frac{x^{2}x}{289}}{64}$$

Express \frac{\frac{x^{2}x}{289}}{64} as a single fraction.

$$\frac{x^{2}x}{289\times 64}$$

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

$$\frac{x^{3}}{289\times 64}$$

Multiply 289 and 64 to get 18496.

$$\frac{x^{3}}{18496}$$