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Exercise

$\left(\sqrt{x-\frac{3}{x}}\right)^{10}$

Step-by-step Solution

1

Simplify $\left(\sqrt{x+\frac{-3}{x}}\right)^{10}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $10$

$\left(x+\frac{-3}{x}\right)^{10\left(\frac{1}{2}\right)}$
2

Multiply the fraction and term in $10\left(\frac{1}{2}\right)$

$x+\frac{-3}{x}^{\frac{10}{2}}$
3

Divide $10$ by $2$

$\left(x+\frac{-3}{x}\right)^{5}$

Final answer to the exercise

$\left(x+\frac{-3}{x}\right)^{5}$

Try other ways to solve this exercise

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Main Topic: Powers of powers

When we have a power inside another power, we can simplify multiplying the exponents: $\left(x^m\right)^n=x^{m\cdot n}$.

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