Question

Which expression is equivalent to 4^1/3 times 4^1/6

Answer 1

The Equation written better:
\[4^{1/3}*4^{1/6}\]

The Choices:
\[A: 2\]
\[B: 16\]
\[C: \sqrt[3]{4}\]
\[D: \sqrt[6]{16}\]

Answer 2

The bases are the same, so you add the exponents.

Answer 3

1/3 + 1/6 = ???

Answer 4

\[\frac{ 1 }{ 3 } + \frac{ 1 }{ 6 } = \frac{ 1 }{ 9 }\]

Answer 5

no

Answer 6

you cannot add the denominators like that

Answer 7

Oh okay that's only with multiplication where you don't have to change the denominators into a common denominator. Oops. Brain fart.
So it's:
\[\frac{ 1 }{ 3 } = \frac{ 2 }{ 6 }\]
\[\frac{ 2 }{ 6 } + \frac{ 1 }{ 6 } = \frac{ 3 }{ 6 } =\frac{ 1 }{ 2 }\]

Answer 8

very good

Answer 9

so "4^1/3 times 4^1/6" turns into 4^(1/2)

Answer 10

anything to the 1/2 power is really taking the square root

that means

\[\Large 4^{1/2} = \sqrt{4}\]

Answer 11

because I'm using the rule

\[\Large x^{m/n} = \sqrt[n]{x^m}\]

Answer 12

Which means that the answer is 2?

Answer 13

correct

Answer 14

Thank you so much!

Answer 15

np