Question

Write 600 as a product of its prime factors in index form

Answer 1

2|600

2|300

2|150

2|75

5|15

5|3

2*2*2*5*5*3 = 600

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Answer 2

Answer:

600 as a product of its prime factors in index form is ${2}^{3} \times {5}^{2} \times 3$

Step-by-step explanation:

Given number is 600.

Here we want to find 600 as a product of its prime factors in index form.

This is a problem of Power of indices.

First we are breaking 600 into prime numbers $600 = 2 \times 2 \times 2 \times 5 \times 3 \times 5$

So,$600 = {2}^{3} \times {5}^{2} \times 3$

600 as a product of its prime factors in index form is ${2}^{3} \times {5}^{2} \times 3$

Here applied formula is $x \times x \times x...... \times n \: times = {x}^{n}$

Some others formulas of power of indices are

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$