Question

Which of the following is equivalent to ^3sqrt(5ab^2) * ^3sqrt(25ab)

Answer 1

The second option is correct

Step-by-step explanation:

Recall,

`\sqrt[a]{b}\text{ = b}^{(1)/(a)}`

Thus, the given expression can be written as

5^(1/3) a^(1/3)b^(2/3) * 5^(2/3)a^(1/3)b^(1/3)

We would apply the rule of exponents which is expressed as

a^b * a^c = a^(b + c)

The expression becomes

5^(1/3) * 5^(2/3) * a^(1/3) * a^1/3 * b^(2/3) * b^(1/3)

= 5^(1/3 + 3/3) * a^(1/3 + 1/3) * b^(2/3 + 1/3)

= 5^(1) * a^(2/3) * b^(1)

= 5 * a^(2/3) * b^(1)

It becomes

`5b\sqrt[3]{a^2}`

The second option is correct