Question

Simplify 6^1/3 times 36^1/3

A. 36
B. 6
C. square root (6)
D. 3^ square root (6)

Answer 1

the simplified form is 6.

B is the correct option.

Explanation:

We have to simplify the expression

`6^(1/3)*36^(1/3)`

We can rewrite this expression using the rule
`x^(1/n)* y^(1/n)=(xy)^(1/n)`

`6^(1/3)*36^(1/3)\\\\=(6*36)^(1/3)\\\\=(216)^(1/3)`

Now, we can write 216 = 6^3

`(216)^(1/3)\\\\=(6^3)^(1/3)`

Now, using the exponent rule
`(x^a)^b=x^(ab)`

`(6^3)^(1/3)=6^{3*(1)/(3)}\\\\=6`

Therefore, the simplified form is 6.

B is the correct option.

Answer 2

6^(1/3) * 36^(1/3) =
( 6 * 36 ) ^(1/3) =
( 6³ ) ^(1/3) =

`= \sqrt[3]{ 6^(3) } =6`
Answer: B ) 6