QuestionWhich expression is equivalent to $\left(2^{\frac{1}{2}}-2^{\frac{3}{4}}\right)^{2}$ ? $\sqrt[4]{2^{3}}$ $\sqrt{2^{5}}$ $\sqrt[4]{4^{3}}$ $\sqrt{4^{5}}$

Studdy Solution
Multiply the results: $$2 \times (1 - 2 \times 2^{\frac{1}{4}} + 2^{\frac{1}{2}})$$
Distribute: $$2 - 4 \times 2^{\frac{1}{4}} + 2 \times 2^{\frac{1}{2}}$$
Simplify: $$2 - 4 \times 2^{\frac{1}{4}} + 2^{\frac{3}{2}}$$
Now compare this expression to the given options.
The expression is equivalent to $\sqrt{2^5}$, which simplifies to $2^{\frac{5}{2}}$.