Question

Simplify the following expression using only positive exponents

Answer 1

Given:

The given expression is
`x^{(3)/(4)} \cdot x^{(5)/(3)}`

We need to simplify the given expression.

Simplification:

Let us simplify the expression using positive exponents.

Let us apply the exponent rule,
`a^(b) \cdot a^(c)=a^(b+c)`

Thus, we have;

`x^{(3)/(4)} x^{(5)/(3)}=x^{(3)/(4)+(5)/(3)}`

Let us simplify the exponent by taking LCM.

Thus, we get;

`x^{(3)/(4)} x^{(5)/(3)}=x^{(9+20)/(12)}`

Simplifying, we get;

`x^{(3)/(4)} x^{(5)/(3)}=x^{(29)/(12)}`

Thus, the simplified value of the given expression is
`x^{(29)/(12)}`

Hence, Option c is the correct answer.