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Evaluate the left hand side to find the value of a in the equation in simplest form. x^((5)/(3))x^((1)/(6))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex53x16=xa x^{\frac{5}{3}} x^{\frac{1}{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.\newlinex53x16=xa x^{\frac{5}{3}} x^{\frac{1}{6}}=x^{a} \newlineAnswer:
  1. Identify and Apply Property: Identify the equation and apply the product of powers property for exponents with the same base: xm×xn=x(m+n)x^m \times x^n = x^{(m+n)}. Here, we have x53×x16x^{\frac{5}{3}} \times x^{\frac{1}{6}}. We need to add the exponents (53)\left(\frac{5}{3}\right) and (16)\left(\frac{1}{6}\right).
  2. Find Common Denominator: To add the fractions 53\frac{5}{3} and 16\frac{1}{6}, find a common denominator. The least common multiple of 33 and 66 is 66. Convert 53\frac{5}{3} to an equivalent fraction with a denominator of 66 by multiplying both the numerator and the denominator by 22.\newline53=(5×2)(3×2)=106\frac{5}{3} = \frac{(5\times2)}{(3\times2)} = \frac{10}{6}.
  3. Add Fractions: Now add the converted fraction 106\frac{10}{6} to 16\frac{1}{6}.\newline106+16=(10+1)6=116.\frac{10}{6} + \frac{1}{6} = \frac{(10+1)}{6} = \frac{11}{6}.
  4. Final Result: We have found that x5/3×x1/6=x11/6x^{5/3} \times x^{1/6} = x^{11/6}. Therefore, the value of aa is 116\frac{11}{6}.

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