simplify the expression by converting to rational exponents. Assume that all variables represent positive real numbers.
5sqrt(x^3)/6sqrt(x^3)=
To simplify the expression by converting to rational exponents, first rewrite the square root as an exponent of 1/2:
5(x^3)^(1/2) / 6(x^3)^(1/2)
Next, simplify the expression by dividing the coefficients and subtracting the exponents:
(5/6)(x^(3/2 - 3/2))
The exponents cancel out, resulting in:
(5/6)(x^0)
Any number raised to the power of 0 is equal to 1, so the final expression simplifies to:
(5/6)(1)
The simplified expression is 5/6.