2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ + 7⁴ + 8⁴ + 9⁴ - 10⁴ =

2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ + 7⁴ + 8⁴ + 9⁴ – 10⁴ =

Pertanyaan:

$tt {2}^{4} + {3}^{4} + {4}^{4} + {5}^{4} + {6}^{4} + {7}^{4} + {8}^{4} + {9}^{4} - {10}^{4} = : ?$

Jawaban dengan langkah-langkah:

$tt {2}^{4} + {3}^{4} + {4}^{4} + {5}^{4} + {6}^{4} + {7}^{4} + {8}^{4} + {9}^{4} - {10}^{4}$

$tt = (2 times 2 times 2 times 2) + (3 times 3 times 3 times 3) + (4 times 4 times 4 times 4) + (5 times 5 times 5 times 5) + (6 times 6 times 6 times 6) + (7 times 7 times 7 times 7) + (8 times 8 times 8 times 8) + (9 times 9 times 9 times 9) - (10 times 10 times 10 times 10)$

$tt = 16 + 81 + 256 + 625 + 1.296 + 2.401 + 4.096 + 6.561 - 10.000$

$tt = 15.332 - 10.000$

$tt = 5.332$

Kesimpulan:

$tt {2}^{4} + {3}^{4} + {4}^{4} + {5}^{4} + {6}^{4} + {7}^{4} + {8}^{4} + {9}^{4} - {10}^{4} = 5.332$

SOAL

2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ + 7⁴ + 8⁴ + 9⁴ – 10⁴ =

PENYELESAIAN

= 2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ + 7⁴ + 8⁴ + 9⁴ – 10⁴

= (2 × 2 × 2 × 2) + (3 × 3 × 3 × 3) + (4 × 4 × 4 × 4) + (5 × 5 × 5 × 5) + (6 × 6 × 6 × 6) + (7 × 7 × 7 × 7) + (8 × 8 × 8 × 8) + (9 × 9 × 9 × 9) – (10 × 10 × 10 × 10)

= (4 × 2 × 2) + (9 × 3 × 3) + (16 × 4 × 4) + (25 × 5 × 5) + (36 × 6 × 6) + (49 × 7 × 7) + (64 × 8 × 8) + (81 × 9 × 9) – (100 × 10 × 10)

= (8 × 2) + (27 × 3) + (64 × 4) + (125 × 5) + (216 × 6) + (343 × 7) + (512 × 8) + (729 × 9) + (1.000 × 10)

= 16 + 81 + 256 + 625 + 1.296 + 2.401 + 4.096 + 6.561 – 10.000

= 97 + 256 + 625 + 1.296 + 2.401 + 4.096 + 6.561 – 10.000

= 353 + 625 + 1.296 + 2.401 + 4.096 + 6.561 – 10.000

= 978 + 1.296 + 2.401 + 4.096 + 6.561 – 10.000

= 2.274 + 2.401 + 4.096 + 6.561 – 10.000

= 4.675 + 4.096 + 6.561 – 10.000

= 8.871 + 6.561 – 10.000

= 15.332 – 10.000

= 5.332