To simplify [tex]\(\sqrt[4]{32}\)[/tex], let's break it down step by step:
1. Express 32 as a power of 2:
[tex]\[ 32 = 2^5 \][/tex]
2. Rewrite the radical expression in terms of exponents:
[tex]\[ \sqrt[4]{32} = \sqrt[4]{2^5} \][/tex]
3. Apply the property of exponents:
Using the property [tex]\(\sqrt[n]{a^m} = a^{m/n}\)[/tex], we can rewrite the expression as:
[tex]\[ \sqrt[4]{2^5} = 2^{5/4} \][/tex]
4. Evaluate the exponent:
To find the value of [tex]\(2^{5/4}\)[/tex], we compute [tex]\(2\)[/tex] raised to the power of [tex]\(\frac{5}{4}\)[/tex].
[tex]\[ 2^{5/4} \approx 2.378414230005442 \][/tex]
Thus, the simplified form of [tex]\(\sqrt[4]{32}\)[/tex] is approximately [tex]\(2.378414230005442\)[/tex].
