The answer is:
[tex]4\sqrt{2}[/tex]
Further explanation:
Given expression is a radical expression. Radical expressions involve fractional exponents.
Given:
[tex]\sqrt[4]{16}\ *\ \sqrt[4]{64}[/tex]
Factorizing 16 and 64
[tex]=\sqrt[4]{2*2*2*2}*\sqrt[4]{2*2*2*2*2*2}\\=\sqrt[4]{2^4} *\sqrt[4]{2^4*2^2}\\Can\ also\ be\ written\ as\\=\sqrt[4]{2^4} *\sqrt[4]{2^4}*\sqrt[4]{2^2}\\={(2^4)}^{\frac{1}{4}}*{(2^4)}^{\frac{1}{4}}*{(2^2)}^{\frac{1}{4}}\\=2*2*{(2)}^{\frac{1}{2} }\\=4*\sqrt{2}\\=4\sqrt{2}[/tex]
The answer is:
[tex]4\sqrt{2}[/tex]
Keywords: Radical expressions, Square root
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