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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^((1)/(2)))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex23x12=xa \frac{x^{\frac{2}{3}}}{x^{\frac{1}{2}}}=x^{a} \newlineAnswer:

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Q. Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex23x12=xa \frac{x^{\frac{2}{3}}}{x^{\frac{1}{2}}}=x^{a} \newlineAnswer:
  1. Simplify Left-hand Side: To solve for aa, we need to simplify the left-hand side of the equation using the properties of exponents.\newlineWhen dividing powers with the same base, we subtract the exponents: xm/xn=x(m−n)x^m / x^n = x^{(m-n)}.\newlineLet's apply this rule to the given expression.
  2. Subtract Exponents: We have x23x^{\frac{2}{3}} divided by x12x^{\frac{1}{2}}.\newlineSubtract the exponents: (23)−(12)\left(\frac{2}{3}\right) - \left(\frac{1}{2}\right).\newlineTo subtract these fractions, we need a common denominator.\newlineThe common denominator for 33 and 22 is 66.
  3. Find Common Denominator: Convert (23)(\frac{2}{3}) and (12)(\frac{1}{2}) to have the common denominator of 66.\newline(23)(\frac{2}{3}) becomes 46\frac{4}{6} and (12)(\frac{1}{2}) becomes 36\frac{3}{6}.\newlineNow subtract the fractions: 46−36=16\frac{4}{6} - \frac{3}{6} = \frac{1}{6}.
  4. Convert Fractions: So, the simplified form of the left-hand side is x16x^{\frac{1}{6}}.\newlineTherefore, a=16a = \frac{1}{6}.\newlineThis is the simplest form of the exponent for the given expression.

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