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

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex52x34=xa \frac{x^{\frac{5}{2}}}{x^{\frac{3}{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.\newlinex52x34=xa \frac{x^{\frac{5}{2}}}{x^{\frac{3}{4}}}=x^{a} \newlineAnswer:
  1. Identify Equation & Apply Quotient Rule: Identify the equation and apply the quotient rule for exponents.\newlineThe quotient rule states that when dividing like bases with exponents, you subtract the exponents: am/an=am−na^{m}/a^{n} = a^{m-n}.\newlineSo, (x5/2)/(x3/4)=x(5/2)−(3/4)(x^{5/2})/(x^{3/4}) = x^{(5/2) - (3/4)}.
  2. Find Common Denominator to Subtract: Find a common denominator to subtract the fractions in the exponents.\newlineThe common denominator for 22 and 44 is 44, so we convert (5/2)(5/2) to (10/4)(10/4) to subtract (3/4)(3/4) from it.\newline$x^{((\(10\)/\(4\)) - (\(3\)/\(4\)))} = x^{(\(7\)/\(4\))}.
  3. Simplify Expression & Find Value: Simplify the expression to find the value of \(a\). The simplified form of the exponent after subtraction is \(\frac{7}{4}\), so \(a = \frac{7}{4}\).

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