Question

simplify ; iv no. with formula​

Answer 1

Solution :-

→ [3^(-4) * 6^(-3) * 25] / [10^(-2) * 16 * 3^(-6)]

→ [3^(-4) * (2*3)^(-3) * 5²] / [(2*5)^(-2) * 2⁴ * 3^(-6)]

using (a * b)^m = a^m * b^m

→ [3^(-4) * 2^(-3) * 3^(-3) * 5²] / [2^(-2) * 5^(-2) * 2⁴ * 3^(-6)]

using a^m * a^n = a^(m + n)

→ [3^(-4 - 3) * 2^(-3) * 5²] / [2^(-2 + 4) * 5^(-2) * 3^(-6)]

→ [3^(-7) * 2^(-3) * 5²] / [2² * 5^(-2) * 3^(-6)]

using a^m ÷ a^n = a^(m - n)

→ 3^(-7 - (-6)) * 2^(-3 - 2) * 5^(2 - (-2))

→ 3^(-7 + 6) * 2^(-5) * 5^(2 + 2)

→ 3^(-1) * 2^(-5) * 5⁴

using a^(-m) = 1/a^m

→ 5⁴/3¹ * 2⁵

→ (625/3 * 32)

→ (625/96) (Ans.)

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