rewrite the expression \\sqrt4{16^{2}} using a fractional exponent. \\sqrt4{16^{2}} = 16^{\\square}…
rewrite the expression \\sqrt4{16^{2}} using a fractional exponent. \\sqrt4{16^{2}} = 16^{\\square} (simplify your answer.)
Answer
Explanation:
Step1: Recall the formula for converting radicals to exponents
The formula is (\sqrt[n]{a^m}=a^{\frac{m}{n}}). Here, (n = 4) (the index of the radical) and (m = 2) (the exponent of the base inside the radical).
Step2: Apply the formula
Substituting (a = 16), (m = 2), and (n = 4) into the formula (\sqrt[n]{a^m}=a^{\frac{m}{n}}), we get (\sqrt[4]{16^{2}}=16^{\frac{2}{4}}).
Step3: Simplify the fraction
Simplify (\frac{2}{4}) to (\frac{1}{2}).
Answer:
(16^{\frac{1}{2}})