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secondary 4 | E Maths
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Tricky indices qn
Date Posted: 2 years ago
Views: 205
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3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, 3⁶ = 729
The pattern for the last digit repeats for every increase of the power by 4 : 3,9,7,1,3,9,7,1,...
8¹ = 8, 8² = 64, 8³ = 512, 8⁴ = 4096, 8⁵ = 32768, 8⁶ = 262144
The pattern for the last digit also repeats every power of 4 : 8,4,2,6,8,4,2,6,...
So, for 3³¹,
31 = 32 - 1 = 4 × 8 - 1
The last power of every set of 4 ends with a 1, so 3³¹ would end with the number before that, which is 7.
For 8¹⁶,
16 = 4 × 4
The last power of every set ends with a 6, so 8¹⁶ ends with a 6.
Finally, for 3³¹ - 8¹⁶, the subtraction of the digits in the ones place will be :
7 - 6 = 1
The last digit is 1.
The pattern for the last digit repeats for every increase of the power by 4 : 3,9,7,1,3,9,7,1,...
8¹ = 8, 8² = 64, 8³ = 512, 8⁴ = 4096, 8⁵ = 32768, 8⁶ = 262144
The pattern for the last digit also repeats every power of 4 : 8,4,2,6,8,4,2,6,...
So, for 3³¹,
31 = 32 - 1 = 4 × 8 - 1
The last power of every set of 4 ends with a 1, so 3³¹ would end with the number before that, which is 7.
For 8¹⁶,
16 = 4 × 4
The last power of every set ends with a 6, so 8¹⁶ ends with a 6.
Finally, for 3³¹ - 8¹⁶, the subtraction of the digits in the ones place will be :
7 - 6 = 1
The last digit is 1.
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