Question

using rational exponents to rewrite expressions - item 50625
what expression has the same meaning as (2^{\frac{7}{4}})?
options: (sqrt4{2^4}), (sqrt7{2^4}), (sqrt4{7^2}), (sqrt{7^4}) (actual options may vary based on image clarity, but the core question is about rewriting (2^{\frac{7}{4}}) using radicals)

Explanation:

Step1: Recall the formula for rational exponents

The formula for converting a rational exponent \(a^{\frac{m}{n}}\) to a radical is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\).

Step2: Apply the formula to \(2^{\frac{7}{4}}\)

Here, \(a = 2\), \(m = 7\), and \(n = 4\). So, \(2^{\frac{7}{4}}=\sqrt[4]{2^{7}}\).

Answer:

\(\sqrt[4]{2^{7}}\) (the option with \(\sqrt[4]{2^{7}}\))