A swimming club uses a scaling factor to order shorter lane ropes whenever a smaller training pool is booked for an away meet, based on comparing the two po...
Question 1 Report
A swimming club uses a scaling factor to order shorter lane ropes whenever a smaller training pool is booked for an away meet, based on comparing the two pool widths. The factor is defined as \(\left(\dfrac{25}{9}\right)^{-\frac12}\). Work out the value of this factor, giving your answer as a fraction. (2)
Answer Details
A negative index means "take the reciprocal", and a power of \(\frac{1}{2}\) means "take the square root". Applying these in either order gives the same result.
Taking the reciprocal of \(\dfrac{25}{9}\) first turns the negative index positive: \(\left(\dfrac{25}{9}\right)^{-\frac12} = \left(\dfrac{9}{25}\right)^{\frac12}\). Taking the square root of the numerator and denominator separately, \(\sqrt{9}=3\) and \(\sqrt{25}=5\), so the scaling factor is \(\dfrac{3}{5}\). [2 marks]
Exam tip: deal with the negative sign in an index (flip the fraction) before dealing with the fractional part (take the root) - doing the flip last makes it easy to lose track of which fraction goes on top.
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