Question

simplify 2 power 3 * 2 power 7 * 4 power 2​

Answer 1

2^3 × 2^7 × 4^2

2^3+7 (a^m × a^n = a^m+n)

2^10 ×4^2

2^10 = 2×2×2×2×2×2×2×2×2×2 = 4×4×4×4×4 =

16×16×4 = 16×64 = 1024

4^2 = 4×4=16

1024×16 = 16384

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Answer 2

We need to simplify the given expression.

Given expression is

${2}^{3} \times {2}^{7} \times {4}^{2} \\ = {2}^{3} \times {2}^{7} \times {( {2}^{2} })^{2}$

We know that

${ ({a}^{m} })^{n} = {a}^{m \times n}$

Let's apply this formula for the last term of the expression.

${2}^{3} \times {2}^{7} \times { ({2}^{2} })^{2} \\ = {2}^{3} \times {2}^{7} \times {2}^{4}$

Now we know that,

${a}^{m} \times {a}^{n} = {a}^{m + n}$

If bases are equal, we can add the powers.

So the expression can be again simplified as

${2}^{3} \times {2}^{7} \times {2}^{4} \\ = {2}^{3 + 7 + 4} \\ = {2}^{14}$

So the given expression can be simplified as

${2}^{3} \times {2}^{7} \times {4}^{2} = {2}^{14}$

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