Question

simplify 6^1/3 times 36^1/3
A. 36
B. 6
C. square root (6)
D. 3^ square root (6)

Answer 1

6^(1/3) * 36^(1/3) = 
( 6 * 36 ) ^(1/3) =
( 6³ ) ^(1/3) =
$= \sqrt[3]{ 6^{3} } =6$
Answer: B ) 6 

Answer 2

Answer:

the simplified form is 6.

B is the correct option.

Step-by-step explanation:

We have to simplify the expression

$6^{1/3}\times36^{1/3}$

We can rewrite this expression using the rule $x^{1/n}\times y^{1/n}=(xy)^{1/n}$

$6^{1/3}\times36^{1/3}\\\\=(6\times36)^{1/3}\\\\=(216)^{1/3}$

Now, we can write 216 = 6^3

$(216)^{1/3}\\\\=(6^3)^{1/3}$

Now, using the exponent rule $(x^a)^b=x^{ab}$

$(6^3)^{1/3}=6^{3\times\frac{1}{3}}\\\\=6$

Therefore, the simplified form is 6.

B is the correct option.