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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^(2))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex52x2=xa \frac{x^{\frac{5}{2}}}{x^{2}}=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.\newlinex52x2=xa \frac{x^{\frac{5}{2}}}{x^{2}}=x^{a} \newlineAnswer:
  1. Apply Quotient Rule: To solve for aa, we need to simplify the left-hand side of the equation using the properties of exponents. Specifically, we will use the quotient rule for exponents, which states that when dividing like bases, we subtract the exponents: xm/xn=x(m−n)x^m / x^n = x^{(m-n)}.
  2. Calculate Exponents: Apply the quotient rule to the expression (x5/2)/(x2)(x^{5/2}) / (x^2). This means we subtract the exponent of the denominator 22 from the exponent of the numerator 5/25/2.\newlineCalculation: (5/2)−2=(5/2)−(4/2)=1/2(5/2) - 2 = (5/2) - (4/2) = 1/2.
  3. Simplify Expression: After simplifying the exponents, we find that x5/2/x2=x1/2x^{5/2} / x^2 = x^{1/2}. Therefore, the value of aa is 1/21/2.

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