First question asks value of 2^x+3
Second and Third questions ask for simplification of equations..
I will post more questions later for those who need to exercise exponents and roots
Good luck !
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Some good examples to Exponents Questions
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Question Number : 1
y = 2^x
Now, 2^(x + 3) = (2^x)*(2^3) = 8*(2^x) = 8y
The correct answer is E.
y = 2^x
Now, 2^(x + 3) = (2^x)*(2^3) = 8*(2^x) = 8y
The correct answer is E.
Last edited by Anurag@Gurome on Mon Feb 04, 2013 10:49 pm, edited 1 time in total.
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Question Number : 2
a^(y - x) = a^(-(x - y) = 1/[a^(x - y)]
Hence, 1/[a^(y - x) + 1] = 1/[1/[a^(x - y)] + 1] = 1/[1 + [a^(x - y)]]/[a^(x - y)] = [a^(x - y)]/[a^(x - y) + 1]
# 1/[a^(x - y) + 1] + 1/[a^(y - x) + 1]
= 1/[a^(x - y) + 1] + [a^(x - y)]/[a^(x - y) + 1]
= [1 + a^(x - y)]/[a^(x - y) + 1]
= 1
The correct answer is C.
a^(y - x) = a^(-(x - y) = 1/[a^(x - y)]
Hence, 1/[a^(y - x) + 1] = 1/[1/[a^(x - y)] + 1] = 1/[1 + [a^(x - y)]]/[a^(x - y)] = [a^(x - y)]/[a^(x - y) + 1]
# 1/[a^(x - y) + 1] + 1/[a^(y - x) + 1]
= 1/[a^(x - y) + 1] + [a^(x - y)]/[a^(x - y) + 1]
= [1 + a^(x - y)]/[a^(x - y) + 1]
= 1
The correct answer is C.
Last edited by Anurag@Gurome on Mon Feb 04, 2013 10:49 pm, edited 1 time in total.
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Question Number : 3
# 3*((a^2)^3) - 2*((a^3)^2) - (a^5)
= 3*(a^6) - 2*(a^6) - a^5
= a^6 - a^5
The correct answer is C.
# 3*((a^2)^3) - 2*((a^3)^2) - (a^5)
= 3*(a^6) - 2*(a^6) - a^5
= a^6 - a^5
The correct answer is C.
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