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Evaluate the left hand side to find the value of a in the equation in simplest form. x^((2)/(3))x^((4)/(5))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex23x45=xa x^{\frac{2}{3}} x^{\frac{4}{5}}=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.\newlinex23x45=xa x^{\frac{2}{3}} x^{\frac{4}{5}}=x^{a} \newlineAnswer:
  1. Identify Equation: Identify the equation and apply the product of powers property.\newlineThe product of powers property states that when multiplying like bases with exponents, you add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlineSo, x23×x45x^{\frac{2}{3}} \times x^{\frac{4}{5}} can be simplified by adding the exponents.
  2. Add Exponents: Add the exponents (23)(\frac{2}{3}) and (45)(\frac{4}{5}).\newlineTo add the fractions, find a common denominator, which in this case is 1515.\newline(23)(\frac{2}{3}) can be written as (23)×(55)=1015(\frac{2}{3})\times(\frac{5}{5}) = \frac{10}{15} and (45)(\frac{4}{5}) can be written as (45)×(33)=1215(\frac{4}{5})\times(\frac{3}{3}) = \frac{12}{15}.\newlineNow add the two fractions: (1015)+(1215)=(10+1215)=2215(\frac{10}{15}) + (\frac{12}{15}) = (\frac{10 + 12}{15}) = \frac{22}{15}.
  3. Find Common Denominator: Write the result as the exponent of xx. The equation now reads x2215x^{\frac{22}{15}}. This means that a=2215a = \frac{22}{15}.

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