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Serjik [45]
2 years ago
13

If A is= 31×37 to the power of 2, how many factors does A have

Mathematics
1 answer:
oksano4ka [1.4K]2 years ago
4 0

Answer:

A has 3 factors: 31 x 37 x 37

Step-by-step explanation:

31 and 37 are prime numbers so there are no other factors. due to the square the factor 37 shows up twice.

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Prove that for any natural n the number 3^(n+4)−3^n is divisible by 16.
gtnhenbr [62]

Answer:

Proved (See Explanation)

Step-by-step explanation:

Show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.

This is done as follows

\frac{3^{n+4} - 3^n}{16}

From laws of indices;

aᵐ⁺ⁿ = aᵐ * aⁿ.

So, 3ⁿ⁺⁴ can be written as 3ⁿ * 3⁴.

\frac{3^{n+4} - 3^n}{16} becomes

\frac{3^n * 3^4 - 3^n}{16}

Factorize

\frac{3^n(3^4 - 1)}{16}

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\frac{3^n(80)}{16}

3ⁿ * 5

5(3ⁿ)

<em>The expression can not be further simplified.</em>

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3 0
3 years ago
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