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10 (a) Write down the value of $10^{ rac{1}{3}}$ - Edexcel - GCSE Maths - Question 10 - 2017 - Paper 1

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10 (a) Write down the value of $10^{ rac{1}{3}}$. (b) Find the value of $125^{ rac{2}{3}}$.

Worked Solution & Example Answer:10 (a) Write down the value of $10^{ rac{1}{3}}$ - Edexcel - GCSE Maths - Question 10 - 2017 - Paper 1

Step 1

Write down the value of $10^{ rac{1}{3}}$

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Answer

The value of 10^{ rac{1}{3}} is the cube root of 10, which can be expressed as: 10^{ rac{1}{3}} = ext{cube root of } 10 Acceptable answers include approximate decimal values (like 2.154) or simply leaving it in radical form.

Step 2

Find the value of $125^{ rac{2}{3}}$

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Answer

To find the value of 125^{ rac{2}{3}}, we can break it down into two steps:

  1. First, find the cube root of 125: 125^{ rac{1}{3}} = 5 because 53=1255^3 = 125.

  2. Now square that result: 52=255^2 = 25

Thus, the value of 125^{ rac{2}{3}} is 25.

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