Final answer:
To express the expression x ²/³. x⁵/⁶ using rational exponents, we can rewrite the exponents as fractions and then simplify the result.
Step-by-step explanation:
To express the expression x ²/³. x⁵/⁶ using rational exponents, we can rewrite the exponents as fractions. The exponent ²/³ can be written as a cube root and the exponent ⁵/⁶ can be written as a sixth root. So, the expression becomes x^(2/3) * x^(5/6).
To multiply the terms with the same base, we add the exponents. Therefore,
x^(2/3) * x^(5/6) = x^((2/3) + (5/6)).
Combining the fractions, we get
x^((4/6) + (5/6)).
Simplifying the fraction gives us
x^(9/6)= x^(3/2).