working out the values of standard form?

Question

i think its standard form anyway...

work out...

i)5^-2 .... i think its 1/25

ii) 27^-1/3

iv) 25^1/2



given that x=2^k and rt.4/x=2^c, find c in terms of k

Answer 1

i)5^(-2) = 1/(5^2) = 1/25

ii) 27^(-1/3) = 1/ [third root of 27] = 1/3

iv) 25^1/2 = square root 25 = 5

-> given that x=2^k and rt.4/x=2^c, find c in terms of k

4/x = 2^c [multiply both sides by x]
4 = x 2^c [write 4=2^2]
2^2 = x 2^c [divide both sides by 2^c]
2^(2-c) = x

So you know that x = 2^(2-c) and x=2^k.
Hence 2^(2-c) = 2^k
2-c = k
c = 2-k

Answer 2

i)5-² = 1/25

ii) 27-¹/³ = ³\/3-³ = 1/3

iv) 25¹/² = \/25 = \/5² = 5
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given that x=2^k and rt.4/x=2^c, find c in terms of k
x = 2^k and x =2^2-c
k = 2-c
::

Answer 3

1.yes it is 1/25

2.1/3

3.5

4/2^k=2^c
4=2^(k+c)
k+c=2
c=-k+2

Answer 4

i) you're correct
ii) 3
iv) 5