1 Answer

Nafiz · Answer 1 · 2020-02-12T20:15:52+0000

Answer:

See explanation

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:
$a^m=a* a* a....m\:\:times$ .

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:

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

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

This gives us:

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

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