(ii) (25 ×5^(2)×t^(8))/(10^(3)×t^(4))

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(ii)  (25 ×5^(2)×t^(8))/(10^(3)×t^(4))

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Identify Given Expression: Identify the given expression and break it down into smaller parts that can be simplified individually. The expression is (25 × 5^(2) × t^(8)) / (10^(3) × t^(4)).Simplify Numerical Part: Simplify the numerical part of the expression by dividing 25 by 10^(3). Since 10^(3) is 10 × 10 × 10, which equals 1000, we can simplify 25 / 1000 to 1 / 40 by dividing both the numerator and the denominator by 25.Simplify Powers of 5: Simplify the powers of 5 by recognizing that 5^(2) is part of the numerator and 10^(3) in the denominator has a factor of 5^(3). Since 10 is 5 × 2, we can rewrite 10^(3) as (5 × 2)^(3), which is 5^(3) × 2^(3). Now we can cancel out 5^(2) from the numerator with part of 5^(3) in the denominator, leaving us with 5^(3-2) in the denominator.Simplify Powers of t: Simplify the powers of t by recognizing that t^(8) is in the numerator and t^(4) is in the denominator. We can divide t^(8) by t^(4) to get t^(8-4), which simplifies to t^(4).Combine Simplified Parts: Combine the simplified parts to form the final simplified expression. We have 1 / 40 from the numerical part, 1 / 5 from the powers of 5, and t^(4) from the powers of t. Multiplying these together, we get (1 / 40) × (1 / 5) × t^(4).Further Simplify Numerical Part: Simplify the numerical part further by multiplying 1 / 40 by 1 / 5. 1 / 40 × 1 / 5 equals 1 / 200.Write Final Expression: Write the final simplified expression. The final simplified expression is (1 / 200) × t^(4), or t^(4) / 200.

(ii) $\frac{25 \times 5^{2} \times t^{8}}{10^{3} \times t^{4}}$

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(ii) 25×52×t8103×t4\frac{25 \times 5^{2} \times t^{8}}{10^{3} \times t^{4}}103×t425×52×t8​

(ii) $\frac{25 \times 5^{2} \times t^{8}}{10^{3} \times t^{4}}$