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2 (a) Simplify fully - OCR - GCSE Maths - Question 2 - 2019 - Paper 5
Question 2
2 (a) Simplify fully. \[ \frac{3a^8 \times 2^5}{a^2} \] (b) Solve. \[ \frac{6x - 10}{5} = 1 \]
Worked Solution & Example Answer:2 (a) Simplify fully - OCR - GCSE Maths - Question 2 - 2019 - Paper 5
Step 1
(a) Simplify fully.
Answer
To simplify the expression ( \frac{3a^8 \times 2^5}{a^2} ), we can proceed as follows:
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Multiply the terms in the numerator: [ 3a^8 \times 2^5 = 3 \times 32 \times a^8 = 96a^8 ]
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Now, write the full expression: [ \frac{96a^8}{a^2} ]
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Use the laws of exponents to simplify: [ a^{8-2} = a^{6} ]
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Combine the results: [ \frac{96a^8}{a^2} = 96a^6 ]
Therefore, the final simplified answer is: [ 96a^6 ]
Step 2
(b) Solve.
Answer
To solve the equation ( \frac{6x - 10}{5} = 1 ), we can follow these steps:
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Eliminate the fraction by multiplying both sides by 5: [ 6x - 10 = 5 ]
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Add 10 to both sides: [ 6x = 15 ]
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Divide each side by 6: [ x = \frac{15}{6} = \frac{5}{2} ]
Thus, the solution for ( x ) is: [ x = \frac{5}{2} ]