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12 (a) Find the value of $81^{ rac{1}{2}}$ - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 1

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12 (a) Find the value of $81^{ rac{1}{2}}$. (b) Find the value of $igg( rac{64}{125} igg)^{ rac{3}{2}}$.

Worked Solution & Example Answer:12 (a) Find the value of $81^{ rac{1}{2}}$ - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 1

Step 1

Find the value of $81^{ rac{1}{2}}$

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Answer

To find the value of 81^{ rac{1}{2}}, we calculate the square root of 81:

81^{ rac{1}{2}} = ext{sqrt}(81) = 9.

Step 2

Find the value of $(\frac{64}{125})^{\frac{3}{2}}$

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Answer

To evaluate (64125)32(\frac{64}{125})^{\frac{3}{2}}, we first take the square root of both the numerator and denominator, and then raise the result to the power of 3:

  1. Calculate the square root: 641212512=85.\frac{64^{\frac{1}{2}}}{125^{\frac{1}{2}}} = \frac{8}{5}.

  2. Raise to the power of 3: (85)3=8353=512125=1625.\bigg(\frac{8}{5}\bigg)^{3} = \frac{8^{3}}{5^{3}} = \frac{512}{125} = \frac{16}{25}.

Thus, the final value is 1625\frac{16}{25}.

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