Question

If 2^x.3^y.5^z=2160, find the values of x, y and z. Hence, compute the value of 3^x.2^(-y).5^(-z).
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Answer 1

Answer:

$2160 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 = {2}^{4} \times {3}^{3} \times {5}^{1}$

now,

${2}^{x} \times {3}^{y} \times {5}^{z} = {2}^{4} \times {3}^{3} \times 5$

so x = 4 , y = 3 , z = 1.

hence,

${3}^{x} \times {2}^{ - y} \times {5}^{ - z} = {3}^{4} \times {2}^{ - 3} \times {5}^{ - 1} = \frac{81}{8 \times 5} = \frac{81}{40}$

Ans.

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