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

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex43x23=xa\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}=x^{a}\newline□ \square

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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.\newlinex43x23=xa\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}=x^{a}\newline□ \square
  1. Simplify using exponent properties: To solve for aa, we need to simplify the left-hand side of the equation using the properties of exponents. When dividing powers with the same base, we subtract the exponents. So, we will subtract the exponent of the denominator from the exponent of the numerator.\newlineCalculation: (43)−(23)=4−23=23.(\frac{4}{3}) - (\frac{2}{3}) = \frac{4 - 2}{3} = \frac{2}{3}.
  2. Equating left and right sides: Now that we have simplified the left-hand side, we can equate it to the right-hand side to find the value of aa. The simplified form of the left-hand side is x23x^{\frac{2}{3}}, so we have x23=xax^{\frac{2}{3}} = x^a. Therefore, aa must be equal to 23\frac{2}{3}.

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