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Evaluate the left hand side to find the value of a in the equation in simplest form. (x^((5)/(6)))^((1)/(4))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x56)14=xa \left(x^{\frac{5}{6}}\right)^{\frac{1}{4}}=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(x56)14=xa \left(x^{\frac{5}{6}}\right)^{\frac{1}{4}}=x^{a} \newlineAnswer:
  1. Apply Power Rule: Apply the power of a power rule to simplify the left-hand side of the equation.\newlineThe power of a power rule states that (xm)n=x(m∗n)(x^m)^n = x^{(m*n)}. Therefore, we can simplify (x(5/6))(1/4)(x^{(5/6)})^{(1/4)} by multiplying the exponents.\newline(x(5/6))(1/4)=x((5/6)∗(1/4))(x^{(5/6)})^{(1/4)} = x^{((5/6)*(1/4))}
  2. Multiply Exponents: Multiply the exponents to find the value of aa.(56)×(14)=524\left(\frac{5}{6}\right) \times \left(\frac{1}{4}\right) = \frac{5}{24}So, (x56)14\left(x^{\frac{5}{6}}\right)^{\frac{1}{4}} simplifies to x524x^{\frac{5}{24}}.
  3. Compare Simplified Forms: Compare the simplified form of the left-hand side to the right-hand side of the equation.\newlineWe have x5/24=xax^{5/24} = x^a, which means that aa must be equal to 5/245/24.

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