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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.

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Answer

To find the prime factorization of 40, we start by dividing it by the smallest prime number: 2.

Divide 40 by 2:

$40 \div 2 = 20$
Divide 20 by 2:

$20 \div 2 = 10$
Divide 10 by 2:

$10 \div 2 = 5$
At this point, 5 is also a prime number and cannot be divided further. Therefore, we can express 40 as the product of its prime factors:

$40 = 2^3 \times 5$

Thus, Azmi's answer of 2 × 2 × 2 × 5 is partially correct, but it should be expressed in index form as 2^3 × 5.

Step 2

Find the value of x.

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Answer

To solve the equation:

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

We can rewrite 1/16 as a power of 2:

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

Now we have:

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

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

$-4 = x$

Therefore, the value of x is:

$x = -4$

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