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Work out $(2 \times 10^{3})^{3} \times (4 \times 10^{1})$, giving your answer in standard form. - OCR - GCSE Maths - Question 1 - 2019 - Paper 5

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Question 1

Work-out-$(2-\times-10^{3})^{3}-\times-(4-\times-10^{1})$,-giving-your-answer-in-standard-form.-OCR-GCSE Maths-Question 1-2019-Paper 5.png

Work out $(2 \times 10^{3})^{3} \times (4 \times 10^{1})$, giving your answer in standard form.

Worked Solution & Example Answer:Work out $(2 \times 10^{3})^{3} \times (4 \times 10^{1})$, giving your answer in standard form. - OCR - GCSE Maths - Question 1 - 2019 - Paper 5

Step 1

Calculate $(2 \times 10^{3})^{3}$

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Answer

To begin, calculate (2×103)3(2 \times 10^{3})^{3}. Using the power of a product property, we can rewrite this as:

(23)×(103)3=8×109(2^{3}) \times (10^{3})^{3} = 8 \times 10^{9}

Step 2

Calculate $(4 \times 10^{1})$

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Answer

Next, we compute the product 4×1014 \times 10^{1}:

4×101=4×10=404 \times 10^{1} = 4 \times 10 = 40

Step 3

Combine the results

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Answer

Now we multiply the results from the previous two steps:

8×109×40=(8×40)×109=320×1098 \times 10^{9} \times 40 = (8 \times 40) \times 10^{9} = 320 \times 10^{9}

To express this in standard form, we rewrite 320320 as 3.2×1023.2 \times 10^{2}, leading to:

3.2×102×109=3.2×10113.2 \times 10^{2} \times 10^{9} = 3.2 \times 10^{11}

Step 4

Final answer in standard form

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Answer

Thus, the final answer in standard form is:

3.2×10113.2 \times 10^{11}

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