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There are two errors in Sam’s method for finding the value of $64^{\frac{2}{3}}$ shown below - OCR - GCSE Maths - Question 15 - 2017 - Paper 1

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There are two errors in Sam’s method for finding the value of $64^{\frac{2}{3}}$ shown below. Find the cube root of 64 and then multiply by 2. The cube root of 64 i... show full transcript

Worked Solution & Example Answer:There are two errors in Sam’s method for finding the value of $64^{\frac{2}{3}}$ shown below - OCR - GCSE Maths - Question 15 - 2017 - Paper 1

Step 1

Describe these errors

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Answer

The first error in Sam’s method is that he incorrectly multiplies the cube root of 64 by 2. The correct approach should involve first squaring the cube root value rather than directly multiplying. The cube root of 64 is indeed 4, but the next step should have been to square this value instead of just multiplying.

The second error is regarding the handling of the power. Sam mentions the negative power but does not apply it correctly. When dealing with powers, a negative exponent indicates the reciprocal. Therefore, instead of getting a negative final answer, one should take the positive value as the answer should be positive.

Step 2

Give the correct value of $64^{\frac{2}{3}}$

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Answer

To correctly calculate 642364^{\frac{2}{3}}, we proceed as follows:

  1. Find the cube root of 64:
    643=4\sqrt[3]{64} = 4
  2. Square the result:
    42=164^2 = 16

Thus, the correct value of 642364^{\frac{2}{3}} is 16.

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