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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form. (9x^(2))/(81x^(4)) Answer:

Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.\newline9x281x4 \frac{9 x^{2}}{81 x^{4}} \newlineAnswer:

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.\newline9x281x4 \frac{9 x^{2}}{81 x^{4}} \newlineAnswer:
  1. Factor out common terms: Factor out common terms in the numerator and the denominator.\newlineThe fraction (9x2)/(81x4)(9x^{2})/(81x^{4}) can be simplified by factoring out common terms. Both the numerator and the denominator have a common factor of 99 and x2x^{2}.
  2. Divide common terms: Divide the common terms.\newlineDivide both the numerator and the denominator by the common factor of 9x29x^{2}.\newline9x281x4=981×x2x4\frac{9x^{2}}{81x^{4}} = \frac{9}{81} \times \frac{x^{2}}{x^{4}}
  3. Simplify numerical part: Simplify the numerical part of the fraction.\newline981\frac{9}{81} simplifies to 19\frac{1}{9}.\newline\left(\frac{\(9\)}{\(81\)}\right) \cdot \left(\frac{x^{\(2\)}}{x^{\(4\)}}\right) = \left(\frac{\(1\)}{\(9\)}\right) \cdot \left(\frac{x^{\(2\)}}{x^{\(4\)}}\right)
  4. Apply laws of exponents: Apply the laws of exponents to simplify the variable part of the fraction.\(\newlineWhen dividing like bases with exponents, subtract the exponents: x2/x4=x2−4=x−2x^{2}/x^{4} = x^{2-4} = x^{-2}.\newline(1/9)×(x2/x4)=(1/9)×x−2(1/9) \times (x^{2}/x^{4}) = (1/9) \times x^{-2}
  5. Write final simplified form: Write the final simplified form of the fraction.\newlineSince x−2x^{-2} is the same as 1/x21/x^{2}, the final simplified form of the fraction is:\newline(1/9)×x−2=1/(9x2)(1/9) \times x^{-2} = 1/(9x^{2})

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