Answer:
40.002
Step-by-step explanation:
[tex]2^{5.322}[/tex] is 2 to the power of 5.322. Only way to find the exact decimal is to calculate in a calculator. When we do so we should get 40.002 as our answer.
The question says:
'If 2^2.322 = 5 then what does 2^5.322 equal? Explain how you found your answer. '
So we have to use the fact that 2^2.322 = 5, in order to work out what 2^5.322 equals
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Remember the following indices rule:
a^m times a^n = a^(m+n)
So first we have to use the indice rule to split apart 2^2.322:
[tex]2^{2.322}=2^{2+0.322}=2^2\times2^{0.322}=4\times2^{0.322}[/tex]
Now we can substitute this into the original equation, and work out the approximate value for [tex]2^{0.322}[/tex]:
[tex]2^{2.322} = 5[/tex]
[tex]4\times2^{0.322}=5[/tex]
[tex]2^{0.322}=\frac{5}{4} =1.25[/tex]
Now lets use the indices rule again to split apart 2^5.322:
[tex]2^{5.322} = 2^{5+0.322}=2^5\times2^{0.322}= 32\times2^{0.322}[/tex]
From the previous equation, we worked out that [tex]2^{0.322} = 1.25[/tex]
Therefore:
[tex]2^{5.322} = 32 \times 1.25 = 40[/tex]
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Answer:
40
