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Evaluate the left hand side to find the value of a in the equation in simplest form. (x^((4)/(5)))^((5)/(3))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x45)53=xa \left(x^{\frac{4}{5}}\right)^{\frac{5}{3}}=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(x45)53=xa \left(x^{\frac{4}{5}}\right)^{\frac{5}{3}}=x^{a} \newlineAnswer:
  1. Identify Equation: Identify the equation to be simplified.\newlineWe have (x4/5)5/3(x^{4/5})^{5/3} and we want to find the value of aa such that (x4/5)5/3=xa(x^{4/5})^{5/3} = x^a.
  2. Apply Power Rule: Apply the power of a power rule.\newlineThe power of a power rule states that (xm)n=x(m∗n)(x^m)^n = x^{(m*n)}. Therefore, we multiply the exponents (45)(\frac{4}{5}) and (53)(\frac{5}{3}) together.
  3. Perform Exponent Multiplication: Perform the multiplication of the exponents.\newline(45)×(53)=(4×55×3)=2015(\frac{4}{5}) \times (\frac{5}{3}) = (\frac{4\times5}{5\times3}) = \frac{20}{15}
  4. Simplify Fraction: Simplify the fraction 2015\frac{20}{15}. 2015\frac{20}{15} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 55. 2015=(20/5)(15/5)=43\frac{20}{15} = \frac{(20/5)}{(15/5)} = \frac{4}{3}
  5. Conclude Value of a: Conclude the value of aa. Since we have simplified the expression to x43x^{\frac{4}{3}}, we can see that a=43a = \frac{4}{3}.

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