Reverse combined integer exponents and compare scientific quantities with unit conversion
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Practise the method.
Reverse combined integer exponents and compare scientific quantities with unit conversion
Reverse combined integer exponents and compare scientific quantities with unit conversion
Example 1
a3=a41.Findx.Fora>0anda=1,(a5)x×a4
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Answer: 8
Combine the indices: 5x+4−3=41.
Solve the linear equation to get x=8.
Example 2
A sample has 2×107 particles. Each particle has mass 6×10−8 grams. The sample is split into 6 equal portions. How many milligrams are in each portion? Use 1 gram =1000 milligrams.
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Answer: 200
The powers give a total mass of 12×10−1 grams.
Convert to milligrams and divide by 6:200 mg.
Example 3
a4=a19.Findx.Fora>0anda=1,(a3)x×a2
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Answer: 7
Combine the indices: 3x+2−4=19.
Solve the linear equation to get x=7.
Put it into practice.
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