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Azmi is given this question - OCR - GCSE Maths - Question 2 - 2021 - Paper 1

Question 2

Azmi is given this question. Write 40 as a product of prime factors. Give your answer in index form. Azmi's answer is 2 × 2 × 2 × 5. Is Azmi correct? Explain your... show full transcript

Worked Solution & Example Answer:Azmi is given this question - OCR - GCSE Maths - Question 2 - 2021 - Paper 1

Step 1

Write 40 as a product of prime factors. Give your answer in index form.

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Answer

To write 40 as a product of prime factors, we start by finding its prime factorization:

Divide 40 by the smallest prime number, which is 2:
- 40 ÷ 2 = 20
Divide 20 by 2:
- 20 ÷ 2 = 10
Divide 10 by 2:
- 10 ÷ 2 = 5
5 is a prime number, so we stop here.

Thus, the prime factorization is:

$40 = 2^3 imes 5$

Azmi's answer of 2 × 2 × 2 × 5 is correct as it simplifies to $2^3 imes 5$ , which is the correct expression in index form.

Step 2

Find the value of x.

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Answer

To find the value of x, we start with the equation:

$\frac{1}{16} = 2^x$

We know that:

$16 = 2^4$

Therefore, we can rewrite 1/16 as:

$\frac{1}{16} = 2^{-4}$

Setting the two expressions equal gives us:

$2^{-4} = 2^x$

Since the bases are the same, we can equate the exponents:

$x = -4$

Thus, the value of x is -4.

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