Question

What is the following product? Assume x greater-than-or-equal-to 0

RootIndex 3 StartRoot x squared EndRoot times RootIndex 4 StartRoot x cubed EndRoot

A. x StartRoot x EndRoot
B. RootIndex 12 StartRoot x Superscript 5 EndRoot
C. x (RootIndex 12 StartRoot x Superscript 5 EndRoot)
D. x6

Answer 1

c

Explanation:

edge 2021

Answer 2

Which is the following product? Assume x ≥ 0

`\sqrt[3]{x^(2)} *\sqrt[4]{x^(3)}`

A.
`x√(x)`

B.
`\sqrt[12]{x^(5)}`

C.
`x\sqrt[12]{x^(5)}`

D.
`x^(6)`

Answer:

C.
`x\sqrt[12]{x^(5)}`

Explanation:

NOTE :
`\sqrt[n]{x^(m)}=x^{(m)/(n)}`

`x^(a)* x^(b)=x^(a+b)`

`\sqrt[3]{x^(2)} *\sqrt[4]{x^(3)}`

`=x^{(2)/(3)}* x^{(3)/(4)}`

`=x^{(2)/(3)+(3)/(4)}`

`=x^{(2*4+3*3)/(12)}`

`=x^{(8+9)/(12)}`

`=x^{(17)/(12)}`

`=x^{(12+5)/(12)}`

`=x^{(12)/(12)+(5)/(12)}`

`=x^{1+(5)/(12)}`

`=x* x^{(5)/(12)}`

`=x\sqrt[12]{x^(5)}`