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14 (a) Work out the value of \( \left( \frac{16}{81} \right)^{\frac{3}{2}} \) (b) Work out the value of \( a + b + c \) - Edexcel - GCSE Maths - Question 15 - 2018 - Paper 1
Question 15
14 (a) Work out the value of \( \left( \frac{16}{81} \right)^{\frac{3}{2}} \) (b) Work out the value of \( a + b + c \)
Worked Solution & Example Answer:14 (a) Work out the value of \( \left( \frac{16}{81} \right)^{\frac{3}{2}} \) (b) Work out the value of \( a + b + c \) - Edexcel - GCSE Maths - Question 15 - 2018 - Paper 1
Step 1
(a) 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 can rewrite this expression using the properties of exponents:
- First, take the square root of the fraction:
[ \sqrt{\frac{16}{81}} = \frac{\sqrt{16}}{\sqrt{81}} = \frac{4}{9} ] - Now raise this result to the power of 3:
[ \left( \frac{4}{9} \right)^{3} = \frac{4^{3}}{9^{3}} = \frac{64}{729} ]
Thus, ( \left( \frac{16}{81} \right)^{\frac{3}{2}} = \frac{64}{729} ).
Step 2
(b) Work out the value of \( a + b + c \)
Answer
To find the values of ( a, b, ) and ( c ), we must analyze the relationships defined:
- We have ( 3^{-2} = \frac{1}{9} ), which implies ( a = -2 ).
- Next, ( 3^{1.5} = 9\sqrt{3} ), therefore ( b = 1.5 ).
- Finally, from ( 3^{-\frac{1}{2}} = \frac{1}{\sqrt{3}} ), we find ( c = -\frac{1}{2} ).
Now, we can sum these values:
[ a + b + c = -2 + 1.5 - 0.5 = -2. ]
Thus, the value of ( a + b + c ) is ( -2 ).