Question

What is the following product? 3 sqrt 16x7 . 3 sqrt 12x9

Answer 1

Answer: The required product is
`4x^5\sqrt[3]{3x}`

Step-by-step explanation: We are given to find the following product :

`P=\sqrt[3]{16x^7}* \sqrt[3]{12x^9}.`

We will be using the following property of exponents :

`(i)~\sqrt[b]{x^a}=x^(a)/(b)\\\\(ii)~x^a* x^b=x^(a+b)\\\\(iii)~x^a* y^a=(xy)^a.`

The required multiplication is as follows :

`P\\\\=\sqrt[3]{16x^7}* \sqrt[3]{12x^9}\\\\=(16x^7)^(1)/(3)* (12x^9)^(1)/(3)\\\\=(16*12* x^(7+9))^(1)/(3)\\\\=(192x^(16))^(1)/(3)\\\\=192^(1)/(3)x^(16)/(3)\\\\=(64*3)^(1)/(3)x^(16)/(3)\\\\=4^{3*(1)/(3)}3^(1)/(3)x^{5+(1)/(3)}\\\\=4* 3^(1)/(3)x^5* x^(1)/(3)\\\\=4x^5\sqrt[3]{3x}.`

Thus, the required product is
`4x^5\sqrt[3]{3x}.`