Question

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

Answer 1

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.