Question

Which is equivalent to 64 Superscript one-fourth?

Answer 1

Answer:

Option 1 - $64^{\frac{1}{4}}=2\sqrt[4]{4}$

Step-by-step explanation:

Given : Expression 64 Superscript one-fourth i.e. $64^{\frac{1}{4}}$

To find : Which is equivalent to expression ?

Solution :

Step 1 - Write the expression,

$64^{\frac{1}{4}}$

Step 2 - Factor the term 64,

$=(2\times 2\times 2\times 2\times 2\times 2)^{\frac{1}{4}}$

$=(2^6)^{\frac{1}{4}}$

$=(2^4\cdot 2^2)^{\frac{1}{4}}$

Step 3 - Apply exponent rule, $(x^a)^{\frac{1}{b}}=x^{\frac{a}{b}}$

$=(2)^{\frac{4}{4}}\cdot (2)^{\frac{2}{4}}$

$=(2)^{1}\cdot (2)^{\frac{2}{4}}$

$=2\cdot 4^{\frac{1}{4}}$

$=2\sqrt[4]{4}$

Therefore, $64^{\frac{1}{4}}=2\sqrt[4]{4}$

So, Option 1 is correct.

Answer 2

Answer:

2 RootIndex 4 StartRoot 4 EndRoot

Step-by-step explanation:

we have

$64^{\frac{1}{4}}$

Decompose the number 64 in prime factors

$64=2^{6}=2^{4}2^{2}$

substitute

$64^{\frac{1}{4}}=(2^{4}2^{2})^{\frac{1}{4}}=2^{\frac{4}{4}}2^{\frac{2}{4}}=2\sqrt[4]{4}$