If P divides a^3 will p divide a

Question

Answer

Off course .

If 4 divides 4096 .
The cube root of 4096 is 16

4096 = 16*16*16 .
Since 4 divides 4096 . It also divides 16.

Hope you get an example .

Th@nk yoû só mûch .

Always be happy forever.

Answer

¥€$_____.

Answer

Ha

Answer

Bilkul .yrr

Answer

Yes for e.g.
if 3 divides 729 (9*9*9)
3 will also divide 9

Answer

Exactly yes

Answer

Yaaaa..

Answer

Yessss

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(1÷3)

Answer

1÷3

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Yes

Answer

Introduction:
If a number p divides another number a^3, we need to determine whether p will also divide a. In this response, we will analyze the relationship between the divisors of a^3 and a and provide a detailed explanation.

Explanation:
To understand whether p will divide a when p divides a^3, we need to consider the prime factorization of a^3 and a.

Prime Factorization of a^3:
The prime factorization of a^3 can be expressed as the product of prime factors raised to their respective powers. Let's represent a^3 as (p1^x1 * p2^x2 * p3^x3 * ... * pn^xn)^3, where p1, p2, p3, ..., pn are prime factors of a and x1, x2, x3, ..., xn are their respective powers.

Prime Factorization of a:
Similarly, the prime factorization of a can be represented as p1^y1 * p2^y2 * p3^y3 * ... * pn^yn, where y1, y2, y3, ..., yn are the respective powers of the prime factors.

Relationship between the Prime Factorization:
Now, let's compare the prime factorizations of a^3 and a to determine the relationship between their divisors:

1. If p divides a^3, it means p must be one of the prime factors in the prime factorization of a^3. So, p must be one of p1, p2, p3, ..., pn.

2. Since p is a prime factor of a^3, it must be raised to a power that is a multiple of 3 in the prime factorization of a^3. Let's assume p = p1. Therefore, p1^x1 is a factor of a^3, and x1 must be divisible by 3.

3. Now, let's examine the prime factorization of a. If p = p1 is a factor of a, then p1^y1 must be present in the prime factorization of a. Since p1^x1 is a factor of a^3 and x1 is divisible by 3, it implies that y1 is also divisible by 3.

Conclusion:
Based on the above analysis, if p divides a^3, and p is a prime factor of a^3, then p must also divide a. This conclusion is derived from the requirement that the prime factorization powers in a and a^3 must be related by being multiples of 3. Therefore, p will divide a when p divides a^3.

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