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

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex2x65=xa \frac{x^{2}}{x^{\frac{6}{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.\newlinex2x65=xa \frac{x^{2}}{x^{\frac{6}{5}}}=x^{a} \newlineAnswer:
  1. Simplify Expression: Simplify the expression on the left-hand side using the properties of exponents.\newlineWhen dividing powers with the same base, subtract the exponents: xm/xn=xm−nx^{m}/x^{n} = x^{m-n}.\newlineSo, (x2)/(x(6)/(5))=x2−(6/5)(x^{2})/(x^{(6)/(5)}) = x^{2 - (6/5)}.
  2. Subtract Exponents: Perform the subtraction of the exponents. \newline2−65=105−65=452 - \frac{6}{5} = \frac{10}{5} - \frac{6}{5} = \frac{4}{5}.\newlineSo, x2x(65)=x45\frac{x^{2}}{x^{\left(\frac{6}{5}\right)}} = x^{\frac{4}{5}}.
  3. Identify Value: Identify the value of aa in the equation.\newlineSince x2x(65)=x45\frac{x^{2}}{x^{\left(\frac{6}{5}\right)}} = x^{\frac{4}{5}}, we have a=45a = \frac{4}{5}.

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