Answer:
2 RootIndex 4 StartRoot 4 EndRoot
Step-by-step explanation:
we have
[tex]64^{\frac{1}{4}}[/tex]
Decompose the number 64 in prime factors
[tex]64=2^{6}=2^{4}2^{2}[/tex]
substitute
[tex]64^{\frac{1}{4}}=(2^{4}2^{2})^{\frac{1}{4}}=2^{\frac{4}{4}}2^{\frac{2}{4}}=2\sqrt[4]{4}[/tex]
Answer:
Option 1 - [tex]64^{\frac{1}{4}}=2\sqrt[4]{4}[/tex]
Step-by-step explanation:
Given : Expression 64 Superscript one-fourth i.e. [tex]64^{\frac{1}{4}}[/tex]
To find : Which is equivalent to expression ?
Solution :
Step 1 - Write the expression,
[tex]64^{\frac{1}{4}}[/tex]
Step 2 - Factor the term 64,
[tex]=(2\times 2\times 2\times 2\times 2\times 2)^{\frac{1}{4}}[/tex]
[tex]=(2^6)^{\frac{1}{4}}[/tex]
[tex]=(2^4\cdot 2^2)^{\frac{1}{4}}[/tex]
Step 3 - Apply exponent rule, [tex](x^a)^{\frac{1}{b}}=x^{\frac{a}{b}}[/tex]
[tex]=(2)^{\frac{4}{4}}\cdot (2)^{\frac{2}{4}}[/tex]
[tex]=(2)^{1}\cdot (2)^{\frac{2}{4}}[/tex]
[tex]=2\cdot 4^{\frac{1}{4}}[/tex]
[tex]=2\sqrt[4]{4}[/tex]
Therefore, [tex]64^{\frac{1}{4}}=2\sqrt[4]{4}[/tex]
So, Option 1 is correct.
