Use a factor tree or repeated division to break 480 into its product of prime factors. E.g.

ed-gcse-maths-pf-hcf-and-lcm-e6a-1

$480 = 2^{5} \times 3 \times 5$

In the same way, 10 can also be broken down into prime factors.

$10^{9} = {(2 \times 5)}^{9}$

Use the index law ${(a b)}^{n} = a^{n} \times b^{n}$ .

^{$10^{9} = 2^{9} \times 5^{9}$}

tree diagram or "2⁵ × 3 × 5" or "2⁹ × 5⁹" [1]

Combine the products of primes of 480 and 10⁹.

$\begin{array}{rcl} 480 \times 10^{9} & = & 2^{5} \times 3 \times 5 \times 2^{9} \times 5^{9} \\ = & 2^{5} \times 2^{9} \times 3 \times 5 \times 5^{9} \end{array}$

Using the index law $a^{m} \times a^{n} = a^{m + n}$ .

$\begin{array}{rcl} 480 \times 10^{9} & = & = 2^{5 + 9} \times 3 \times 5^{1 + 9} \end{array}$

Answer $\begin{array}{rcl} = & 2^{14} \times 3 \times 5^{10} \end{array}$

2^m × 3 × 5ⁿ where m and n are positive integers [1]
fully correct answer [1]

Prime Factors, HCF & LCM (Edexcel IGCSE Maths)

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