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Evaluate the left hand side to find the value of a in the equation in simplest form. (x^(3))/(x^((1)/(4)))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex3x14=xa \frac{x^{3}}{x^{\frac{1}{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.\newlinex3x14=xa \frac{x^{3}}{x^{\frac{1}{4}}}=x^{a} \newlineAnswer:
  1. Identify Equation & Properties: Identify the equation and the properties of exponents to be used.\newlineWe have the equation x3x14=xa\frac{x^{3}}{x^{\frac{1}{4}}}=x^{a}. To simplify the left-hand side, we will use the property of exponents that states when dividing like bases, we subtract the exponents: aman=am−n\frac{a^{m}}{a^{n}} = a^{m-n}.
  2. Apply Exponent Property: Apply the property of exponents to subtract the exponents. x3x14=x3−14\frac{x^{3}}{x^{\frac{1}{4}}} = x^{3 - \frac{1}{4}}
  3. Perform Exponent Subtraction: Perform the subtraction of the exponents. 3−(14)=124−14=1143 - \left(\frac{1}{4}\right) = \frac{12}{4} - \frac{1}{4} = \frac{11}{4}
  4. Write Result as Exponent: Write the result as the exponent of xx.x3−(14)=x114x^{3 - (\frac{1}{4})} = x^{\frac{11}{4}}
  5. Set Expression Equal to xax^a: Set the simplified expression equal to x(a)x^{(a)} to find the value of 'aa'.\newlinex(11/4)=x(a)x^{(11/4)} = x^{(a)}
  6. Determine Value of 'a': Since the bases are the same and the expressions are equal, the exponents must be equal.\newlineTherefore, a=114a = \frac{11}{4}

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