To write the expression [tex]\(\sqrt[4]{15^7}\)[/tex] in the form [tex]\(a^{\frac{b}{c}}\)[/tex], we will follow these steps:
1. Recognize the fourth root notation: The expression [tex]\(\sqrt[4]{15^7}\)[/tex] can be rewritten using the fractional exponent rule. The [tex]\(n\)[/tex]th root of [tex]\(x\)[/tex] can be written as [tex]\(x^{\frac{1}{n}}\)[/tex].
[tex]\[
\sqrt[4]{15^7} = (15^7)^{\frac{1}{4}}
\][/tex]
2. Simplify the exponent: When raising a power to another power, you multiply the exponents. Thus, we rewrite [tex]\((15^7)^{\frac{1}{4}}\)[/tex] by multiplying the exponents [tex]\(7\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
(15^7)^{\frac{1}{4}} = 15^{\frac{7}{4}}
\][/tex]
3. Identify the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]: From the expression [tex]\(15^{\frac{7}{4}}\)[/tex], we can see:
- The base [tex]\(a\)[/tex] is [tex]\(15\)[/tex]
- The numerator of the exponent [tex]\(b\)[/tex] is [tex]\(7\)[/tex]
- The denominator of the exponent [tex]\(c\)[/tex] is [tex]\(4\)[/tex]
Thus, for the expression [tex]\(\sqrt[4]{15^7}\)[/tex],
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 7\)[/tex]
- [tex]\(c = 4\)[/tex]
The correct values to select are:
[tex]\[ a = 15 ,\ b = 7 ,\ c = 4 \][/tex]
