Theory question 102
Indices(a) Simplify (1/35n) × 9n−1 × 27n+1
(b) The sum of the ages of a woman and her daughter is 46 years. In 4 years time, the ratio of their ages will be 7:2. Find their present ages.
Show the model answer
Model answer
(a) Write everything as powers of 3: 3−5n × 32n−2 × 33n+3 = 3−5n + 2n − 2 + 3n + 3 = 31 = 3.
(b) w + d = 46 and (w + 4)/(d + 4) = 7/2, so 2w + 8 = 7d + 28, i.e. 2w − 7d = 20.
Substitute w = 46 − d: 92 − 9d = 20, d = 8 and w = 38.
The woman is 38 and the daughter is 8.
Explanation
Change 9 and 27 to powers of 3 and add the indices.