Answer:
See explanation
Step-by-step explanation:
We want to show that [tex](2\cdot 3\cdot 7)^4=2^4\cdot3^4 \cdot7^4[/tex].
We take the LHS and rewrite to obtain the RHS.
Recall that: [tex]a^m=a\times a\times a....m\:\:times[/tex].
This implies that:
[tex](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)[/tex]
We regroup to get:
[tex](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[/tex]
Apply this rule: [tex]a\times a\times a....m\:\:times=a^m[/tex].
This gives us:
[tex](2\cdot 3\cdot 7)^4=2^4\cdot3^4 \cdot7^4[/tex]...as required.
