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Simplify. Express your answer using positive exponents.\newline5p25p3\frac{5p^2}{5p^3}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline5p25p3\frac{5p^2}{5p^3}
  1. Divide Coefficients and Subtract Exponents: Simplify the expression by dividing the coefficients and subtracting the exponents of like bases.\newline5p25p3=55⋅p2p3\frac{5p^2}{5p^3} = \frac{5}{5} \cdot \frac{p^2}{p^3}
  2. Divide Coefficients: Divide the coefficients. Since 55 divided by 55 is 11, this part of the expression simplifies to 11. \newline55=1\frac{5}{5} = 1
  3. Subtract Exponents of pp: Subtract the exponents of pp. When dividing powers with the same base, we subtract the exponents.p2p3=p(2−3)=p−1\frac{p^2}{p^3} = p^{(2-3)} = p^{-1}
  4. Rewrite Negative Exponent: Since the expression is supposed to be expressed with positive exponents, we rewrite p−1p^{-1} as 1p\frac{1}{p}.\newlinep−1=1pp^{-1} = \frac{1}{p}
  5. Combine Results: Combine the results from Step 22 and Step 44 to write the final simplified expression.\newline1×(1p)=1p1 \times \left(\frac{1}{p}\right) = \frac{1}{p}

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