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9 (a) Express \( \sqrt{10^{100}} \times 10^0 \) as a power of 10 - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 3
Question 10
9 (a) Express \( \sqrt{10^{100}} \times 10^0 \) as a power of 10. Liam was asked to express \( (12^y) \) as a power of 12 Liam wrote \( (12^y) = 12^2 = 12^{2y} \) L... show full transcript
Worked Solution & Example Answer:9 (a) Express \( \sqrt{10^{100}} \times 10^0 \) as a power of 10 - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 3
Step 1
Express \( \sqrt{10^{100}} \times 10^0 \) as a power of 10
Answer
To express ( \sqrt{10^{100}} \times 10^0 ) as a power of 10, we first deal with the square root:
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Recall that ( \sqrt{x} = x^{1/2} ). Thus, ( \sqrt{10^{100}} = (10^{100})^{1/2} = 10^{100 \times \frac{1}{2}} = 10^{50} ).
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Next, we multiply this by ( 10^0 ), which is 1. Therefore:
[ 10^{50} \times 10^0 = 10^{50 + 0} = 10^{50}. ]
So the final answer is ( 10^{50} ).
Step 2
Explain why Liam's method is wrong.
Answer
Liam's method is incorrect because he misunderstood the properties of exponents. He wrote that ( (12^y) = 12^2 = 12^{2y} ), which implies he incorrectly treated ( y ) as if it were a constant factor that could be distributed inside the exponent using addition.
The correct approach should have maintained the variable ( y ) properly. The expression ( 12^y ) should remain as ( 12^y ), and not be assumed to equal ( 12^2 ). Hence,
- The correct expression is still ( 12^y ).
- Additionally, you cannot simply multiply or add exponents without proper context. In this case, it should have been calculated as ( 12^y = 12^y ).
Thus, Liam did not apply the rules of exponents correctly.