Let's break down the expression [tex]\(7^{\frac{2}{4}}\)[/tex] and rewrite it in the form [tex]\(\sqrt[c]{a^b}\)[/tex].
1. Observe that [tex]\(7^{\frac{2}{4}}\)[/tex] can be simplified as [tex]\(7^{\frac{1}{2}}\)[/tex]. This is because [tex]\(\frac{2}{4}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
2. Recall that the notation [tex]\(7^{\frac{1}{2}}\)[/tex] is another way of writing [tex]\(\sqrt{7}\)[/tex], which corresponds to [tex]\(\sqrt[2]{7^1}\)[/tex].
So, matching this to the form [tex]\(\sqrt[c]{a^b}\)[/tex],
- [tex]\(a = 7\)[/tex] because the base of the original expression remains the same,
- [tex]\(b = 1\)[/tex] because the numerator of the exponent indicates the power of the base inside the root,
- [tex]\(c = 2\)[/tex] because the denominator of the exponent indicates the root.
Therefore, for the expression [tex]\(7^{\frac{2}{4}}\)[/tex],
- [tex]\(a = 7\)[/tex],
- [tex]\(b = 1\)[/tex],
- [tex]\(c = 2\)[/tex].
Thus:
- [tex]\(a = 7\)[/tex],
- [tex]\(b = 1\)[/tex],
- [tex]\(c = 2\)[/tex].
