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14 (a) Work out the value of $$\left( \frac{16}{81} \right)^{\frac{3}{2}}$$ (2) (b) Work out the value of a + b + c (2) - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 1
Question 14
14 (a) Work out the value of $$\left( \frac{16}{81} \right)^{\frac{3}{2}}$$ (2) (b) Work out the value of a + b + c (2)
Worked Solution & Example Answer:14 (a) Work out the value of $$\left( \frac{16}{81} \right)^{\frac{3}{2}}$$ (2) (b) Work out the value of a + b + c (2) - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 1
Step 1
Work out the value of \( \left( \frac{16}{81} \right)^{\frac{3}{2}} \)
Answer
To solve ( \left( \frac{16}{81} \right)^{\frac{3}{2}} ), we first find the square root of ( \frac{16}{81} ) and then raise the result to the power of 3.
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Calculate the square root: [ \sqrt{\frac{16}{81}} = \frac{\sqrt{16}}{\sqrt{81}} = \frac{4}{9} ]
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Now raise to the power of 3: [ \left( \frac{4}{9} \right)^3 = \frac{4^3}{9^3} = \frac{64}{729} ]
Hence, ( \left( \frac{16}{81} \right)^{\frac{3}{2}} = \frac{64}{729} ).
Step 2
Work out the value of a + b + c
Answer
To calculate the values of a, b, and c, we start from the given equations:
- Given: ( 3^{-2} = \frac{1}{9} )
- ( 3^{2} = 9 = \sqrt{3}^4 )
- ( 3^{-\frac{1}{2}} = \frac{1}{\sqrt{3}} ) which simplifies to 1.
Counting valid solutions for a, b, and considering the context, we conclude:
[ a + b + c = 3 - 3 + 1 = 1 ]