Question

Evaluate: 64 ^1/3

A) 3
B) 4
C) 6
D) 8

Answer 1

(B) 4

Explanation:

`64 ^(1)/(3) \\\\\mathrm{Factor\:the\:number:\:}\:64=4^3\\\\=\left(4^3\right)^{(1)/(3)}\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^(bc),\:\quad \:a\ge 0\\\\\left(4^3\right)^{(1)/(3)}=4^{3*(1)/(3)}\\\\3*(1)/(3)=1\\\\=4^1\\\\=4`

Answer 2

`\text{Hey there!}`

`\bf{(64)^ {(1)/(3)}}`

`= \bf{\sqrt[3]{64^1} }`

`\bf{√(64^1) \ \rightarrow 64}`

`\sqrt[3]{64}`

`√(64)= 8`

`\bf{We\ solve\ half\ of\ 8 \ by\ dividing\ 8\ from\ 2 \ like: (8)/(2)}`

`\bf{(8/2)/(2/2) = (4)/(1) = 4 }`

`\bf{Thus, \ your\ answer\ is: \boxed{\bf{B. \ 4}}}\checkmark`

`\text{Good luck on your assignment and enjoy your day!}`

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`\frak{LoveYourselfFirst:)}`