Simplify \(\frac{20p^{5}q^{8}}{4p^{-2}q^{3}}\).
Question 1 Report
Simplify \(\frac{20p^{5}q^{8}}{4p^{-2}q^{3}}\).
Answer Details
Simplify the number part and each letter separately, using \( \frac{x^{m}}{x^{n}} = x^{m-n} \) throughout.
- Numbers: \( 20 \div 4 = 5 \).
- The \( p \) terms: \( \dfrac{p^{5}}{p^{-2}} = p^{5-(-2)} = p^{7} \). Subtracting a negative index adds, so the index grows.
- The \( q \) terms: \( \dfrac{q^{8}}{q^{3}} = q^{8-3} = q^{5} \).
The answer is \( 5p^{7}q^{5} \) [B3], awarded as one mark each for the \( 5 \), the \( p^{7} \) and the \( q^{5} \).
The \( p \) term is the discriminating part. A helpful way to see it is that \( p^{-2} \) in the denominator equals \( \dfrac{1}{p^{2}} \), and dividing by \( \dfrac{1}{p^{2}} \) multiplies by \( p^{2} \), turning \( p^{5} \) into \( p^{7} \). Answering \( p^{3} \) means the negative sign was dropped.
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