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valentinak56 [21]
3 years ago
11

Show (prove) in detail why (2.3.7)4 = 24 34 74.

Mathematics
1 answer:
GalinKa [24]3 years ago
5 0

Answer:

See explanation

Step-by-step explanation:

We want to show that (2\cdot 3\cdot 7)^4=2^4\cdot3^4 \cdot7^4.

We take the LHS and rewrite to obtain the RHS.

Recall that: a^m=a\times a\times a....m\:\:times.

This implies that:

(2\cdot 3\cdot 7)^4=(2\cdot 3\cdot 7)(2\cdot 3\cdot 7)(2\cdot 3\cdot 7) (2\cdot 3\cdot 7)

We regroup to get:

(2\cdot 3\cdot 7)^4=2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 7\times 7\times 7\times 7

Apply this rule: a\times a\times a....m\:\:times=a^m.

This gives us:

(2\cdot 3\cdot 7)^4=2^4\cdot3^4 \cdot7^4...as required.

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