Now,we express 98 as the sum or difference of two numbers whose powers are easier to calculate, and then use Binomial Theorem. Write 98 = 100 – 2 Thus,(98)5 = (100-2)^5 = 5C0 (100)5 – 5C1 (100)4.2 + 5C2 (100)322 - 5C3(100)2 (2)3 + 5C4 (100) (2)4 – 5C5 (2)5 = 10000000000 – 5 100000000 2 + 10 1000000 4 – 10 10000 8 + 5 100 16 – 32 = 10040008000 – 1000800032 = 9039207968.

Compute (98)5.

Question

Compute (98)⁵.

✓

Answer

Now,we express 98 as the sum or difference of two numbers whose powers are easier to calculate, and then use Binomial Theorem.
Write 98 = 100 – 2
Thus,(98)⁵ = $(100-2)^5$
= ⁵C₀ (100)⁵ – ⁵C₁ (100)⁴.2 + ⁵C₂ (100)³2² - ⁵C₃(100)² (2)³ + ⁵C₄ (100) (2)⁴ – ⁵C₅ (2)⁵
= 10000000000 – 5 $\times$ 100000000 $\times$ 2 + 10 $\times$ 1000000 $\times$ 4 – 10 $\times$10000 $\times$ 8 + 5 $\times$ 100 $\times$ 16 – 32
= 10040008000 – 1000800032 = 9039207968.

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