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Question
If `2^x xx3^yxx5^z=2160,` find x, y and z. Hence, compute the value of `3^x xx2^-yxx5^-z.`
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Solution
Given `2^x xx3^yxx5^z=2160`
First, find out the prime factorisation of 2160.
It can be observed that 2160 can be written as `2^4xx3^3xx5^1`
Also,
`2^x xx36yxx5^z=2^4xx3^3xx5^1`
⇒ x = 4, y = 3, z = 1
Therefore, the value of `3^x xx2^-yxx5^-z` is `3^4xx2^-3xx5^-1=81xx1/8xx1/5=81/40`
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