Question

If x>0, then x^(3/4)/x^(-¼)
HELPP PLEASEEE

Answer 1

`\large\text{$\frac{x^{\left((3)/(4)\right)}}{x^{\left(-(1)/(4)\right)}}=x$}`

Explanation:

Given expression:

`\large\text{$\frac{x^{\left((3)/(4)\right)}}{x^{\left(-(1)/(4)\right)}}$}`

`\textsf{Apply exponent rule} \quad (a^b)/(a^c)=a^(b-c):`

`\implies \large\text{$x^{\left((3)/(4)-\left(-(1)/(4)\right)\right)}$}`

Simplify:

`\implies \large\text{$x^{\left((3)/(4)+(1)/(4)\right)}$}`

`\implies \large\text{$x^{\left((4)/(4)\right)}$}`

`\implies \large\text{$x^(1)$}`

`\textsf{Apply exponent rule} \quad a^1=a:`

`\implies \large\text{$x$}`

Answer 2

x

Explanation:

using the rule of exponents

`(a^(m) )/(a^(n) )` =
`a^((m-n))`

given

`\frac{x^{(3)/(4) } }{x^{-(1)/(4) } }`

=
`x^{(3)/(4)-(-(1)/(4)) }`

=
`x^{((3)/(4)+(1)/(4)) }`

=
`x^(1)`

= x