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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}}=

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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}}=
  1. Simplify Coefficient: First, let's simplify the coefficient by dividing 1212 by 44. \newline124=3\frac{12}{4} = 3\newlineSo, we have 3×x/x33 \times \sqrt{x} / x^{3}.
  2. Express x\sqrt{x}: Now, let's express x\sqrt{x} as x12x^{\frac{1}{2}}.\newlineSo, the expression becomes 3×x12/x33 \times x^{\frac{1}{2}} / x^{3}.
  3. Divide Exponents: Next, we'll use the properties of exponents to divide x1/2x^{1/2} by x3x^{3}. When we divide exponents with the same base, we subtract the exponents: x1/2/x3=x1/2−3x^{1/2} / x^{3} = x^{1/2 - 3}.
  4. Final Expression: Subtracting the exponents gives us x(−5/2)x^{(-5/2)}.\newlineSo, the expression is now 3×x(−5/2)3 \times x^{(-5/2)}.

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