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Evaluate the left hand side to find the value of a in the equation in simplest form. (x^((3)/(2)))^((5)/(6))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x32)56=xa \left(x^{\frac{3}{2}}\right)^{\frac{5}{6}}=x^{a} \newlineAnswer:

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Full solution

Q. Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x32)56=xa \left(x^{\frac{3}{2}}\right)^{\frac{5}{6}}=x^{a} \newlineAnswer:
  1. Simplify the left-hand side: We need to simplify the left-hand side of the equation (x(3/2))(5/6)(x^{(3/2)})^{(5/6)} to find the value of aa. According to the power of a power rule, when we raise a power to another power, we multiply the exponents.\newlineSo, (x(3/2))(5/6)=x((3/2)∗(5/6))(x^{(3/2)})^{(5/6)} = x^{((3/2)*(5/6))}.
  2. Perform fraction multiplication: Now, we perform the multiplication of the fractions (32)(\frac{3}{2}) and (56)(\frac{5}{6}).(32)∗(56)=(3×52×6)=1512.\left(\frac{3}{2}\right) * \left(\frac{5}{6}\right) = \left(\frac{3\times5}{2\times6}\right) = \frac{15}{12}.
  3. Simplify the fraction: We can simplify the fraction 1512\frac{15}{12} by dividing both the numerator and the denominator by their greatest common divisor, which is 33.\newline1512=(15/3)(12/3)=54\frac{15}{12} = \frac{(15/3)}{(12/3)} = \frac{5}{4}.
  4. Determine the value of aa: Now we have x54x^{\frac{5}{4}} on the left-hand side, which means aa must be equal to 54\frac{5}{4} for the equation to be true.\newlineSo, a=54a = \frac{5}{4}.

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