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Express the following fraction in simplest form using only positive exponents. (15w^(3))/((3w)^(2)) Answer:

Express the following fraction in simplest form using only positive exponents.\newline15w3(3w)2 \frac{15 w^{3}}{(3 w)^{2}} \newlineAnswer:

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Full solution

Q. Express the following fraction in simplest form using only positive exponents.\newline15w3(3w)2 \frac{15 w^{3}}{(3 w)^{2}} \newlineAnswer:
  1. Simplify Fraction: Simplify the fraction by dividing the numerator by the denominator.\newlineGiven the fraction (15w3)/((3w)2)(15w^{3})/((3w)^{2}), we can simplify it by dividing the coefficients and subtracting the exponents of like bases according to the quotient rule of exponents.\newline(15w3)/((3w)2)=(15/3)⋅(w3−2)(15w^{3})/((3w)^{2}) = (15/3) \cdot (w^{3-2})
  2. Perform Division: Perform the division and subtraction.\newline(153)×(w3−2)=5×w1(\frac{15}{3}) \times (w^{3-2}) = 5 \times w^{1}
  3. Write Final Expression: Write the final simplified expression.\newlineThe fraction is now simplified to 5w5w.

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