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25 Jan 2026, 22:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
71% (02:50) correct
29%
(02:44)
wrong
based on 161
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If \((\frac{1}{50})^a(\frac{1}{20})^4 = \frac{1}{50} (100)^{-6}\), a = ?
A. 3
B. 4
C. 5
D. 6
E. 7
A. 3
B. 4
C. 5
D. 6
E. 7
25 Jan 2026, 23:44
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We know:
50 = 5^2 * 2
20 = 2^2 * 5
100 = 2^2 * 5^2
L.H.S. of the equation = (2^-1 * 5^-2)^a * (2^-2 * 5^-1)^4 = 2^-(a+8) * 5^-(2a+4)
R.H.S. of the equation = (2^-1 * 5^-2) * (2^-12 * 5^-12) = 2^-13 * 5^-14
Equating the powers of both sides we get:
a+8 = 13, thus, a = 5
2a+4 = 14, thus, a = 5
Hence, the correct answer is Option C - 5
Hope this helps!
50 = 5^2 * 2
20 = 2^2 * 5
100 = 2^2 * 5^2
L.H.S. of the equation = (2^-1 * 5^-2)^a * (2^-2 * 5^-1)^4 = 2^-(a+8) * 5^-(2a+4)
R.H.S. of the equation = (2^-1 * 5^-2) * (2^-12 * 5^-12) = 2^-13 * 5^-14
Equating the powers of both sides we get:
a+8 = 13, thus, a = 5
2a+4 = 14, thus, a = 5
Hence, the correct answer is Option C - 5
Hope this helps!
26 Jan 2026, 05:24
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{ 1/ (2 * 5)^a }* 1 / (2^2 * 5 )^4 = 1/ (2*5^2) {(5)^2 (2)^2}^6
{1/2^a* 5^2a }* { 1/2^8 * 5^4 } = 1/ 2^13 * 5^14
1/ 2^a+8 * 5^2a+4 = 1 / 2^13 * 5^14
a+ 8 = 13
a = 5
{1/2^a* 5^2a }* { 1/2^8 * 5^4 } = 1/ 2^13 * 5^14
1/ 2^a+8 * 5^2a+4 = 1 / 2^13 * 5^14
a+ 8 = 13
a = 5
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