Using exponent rules we can rewrite our expression into:
[tex]\sqrt{x} \sqrt[4]{x} = \sqrt[4]{x^3}[/tex]
Here we need to remember two relations for exponents:
√a = a^(1/2)
(a^n)^m = a^{n*m}
(a^n)*(a^m) = a^{n + m}
Now we can use that to rewrite our expression as:
[tex]\sqrt{x} \sqrt[4]{x} = x^{1/2}*x^{1/4}[/tex]
Now, using the second relation we can simplify the exponent:
[tex]\sqrt{x} \sqrt[4]{x} = x^{1/2}*x^{1/4} = x^{1/2 + 1/4} = x^{3/4} = \sqrt[4]{x^3}[/tex]
If you want to learn more about exponents:
https://brainly.com/question/847241
#SPJ1
