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matrenka [14]
2 years ago
5

Rewrite using a single positive exponent

Mathematics
1 answer:
fiasKO [112]2 years ago
5 0

Step-by-step explanation:

\frac{ {7}^{4} }{7}  =  {7}^{4 - 1}  =  {7}^{3}

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Rewrite the expression in the form 2n​
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Which of the following could not be a value of n? side lengths of 9 and 13
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When the rate of change varies from point to point, the relationship is a
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8 0
2 years ago
Read 2 more answers
Use an induction proof to prove this statement:<br> For n≥1, 4^n+5 is divisible by 3.
Tpy6a [65]

Answer:

See below

Step-by-step explanation:

We shall prove that for all n\in\mathbb{N},3|(4^n+5). This tells us that 3 divides 4^n+5 with a remainder of zero.

If we let n=1, then we have 4^{1}+5=9, and evidently, 9|3.

Assume that 4^n+5 is divisible by 3 for n=k, k\in\mathbb{N}. Then, by this assumption, 3|(4^n+5)\Rightarrow4^k+5=3m,\: m\in\mathbb{Z}.

Now, let n=k+1. Then:

4^{k+1}+5=4^k\cdot4+5\\=4^k(3+1)+5\\=3\cdot4^k+4^k+5\\=3\cdot4^k+3m\\=3(4^k+m)

Since 3|(4^k+m), we may conclude, by the axiom of induction, that the property holds for all n\in\mathbb{N}.

3 0
2 years ago
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