How do you simplify sqrtx^3 timesroot3(x^2)x3×3x2 and write it in exponential form?

1 Answer
May 1, 2016

x^(13/6)x136 assuming x >= 0x0

Explanation:

If x >= 0x0 then (x^a)^b = x^(ab)(xa)b=xab

and x^a xx x^b = x^(a+b)xa×xb=xa+b

Another way of writing root(n)(x)nx is x^(1/n)x1n

So:

sqrt(x)^3 xx root(3)(x^2)x3×3x2

=(x^(1/2))^3 xx (x^2)^(1/3)=(x12)3×(x2)13

=x^(1/2*3) xx x^(2*1/3)=x123×x213

=x^(3/2) xx x^(2/3)=x32×x23

=x^(3/2+2/3)=x32+23

=x^(9/6+4/6)=x96+46

=x^(13/6)=x136