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Rewrite the expression in the form k*x^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). (12sqrtx)/(4x^(3))=◻

Rewrite the expression in the form k⋅xn k \cdot x^{n} .\newlineWrite the exponent as an integer, fraction, or an exact decimal (not a mixed number).\newline12x4x3=□ \frac{12 \sqrt{x}}{4 x^{3}}=\square

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Full solution

Q. Rewrite the expression in the form k⋅xn k \cdot x^{n} .\newlineWrite the exponent as an integer, fraction, or an exact decimal (not a mixed number).\newline12x4x3=□ \frac{12 \sqrt{x}}{4 x^{3}}=\square
  1. Simplify Coefficient: Simplify the coefficient.\newlineDivide the coefficient in the numerator by the coefficient in the denominator.\newlineCalculation: 12/4=312 / 4 = 3
  2. Rewrite as Exponent: Rewrite the square root of xx as an exponent.\newlineThe square root of xx can be written as x(1/2)x^{(1/2)}.
  3. Combine Exponents: Combine the exponents.\newlineWhen dividing powers with the same base, subtract the exponents.\newlineCalculation: (12)−3=(12)−(62)=−52(\frac{1}{2}) - 3 = (\frac{1}{2}) - (\frac{6}{2}) = -\frac{5}{2}
  4. Write Final Expression: Write the final expression.\newlineCombine the simplified coefficient and the combined exponent.\newlineFinal expression: 3x−523x^{-\frac{5}{2}}

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