Question

27 ka power minus 2 by 3 into 81 power 5 by 4 divided by 1 by 3 ki power minus 3

Answer 1

$\frac{ {27}^{ \frac{ - 2}{3}} \times {81}^{ \frac{5}{4} } }{ {( \frac{1}{3} })^{ - 3} } \\ = \frac{ \sqrt[3]{( {27)}^{ - 2} } \times \sqrt[4]{( {81)}^{5} } }{ {3}^{3} } \\ = \frac{ {3}^{ - 2} \times {3}^{5} }{ {3}^{3} } \\ = \frac{ {3}^{3} }{ {3}^{3} } \\ = {3}^{0} \\ = 1$

Answer 2

Given  :  27 ka power minus 2 by 3 into 81 power 5 by 4 divided by 1 by 3 ki power minus 3

$\dfrac{(27)^{-\frac{2}{3}} (81)^{\frac{5}{4} }}{ (\dfrac{1}{3})^{-3} }$

To Find  : Simplify

Solution:

$\dfrac{(27)^{-\frac{2}{3}} (81)^{\frac{5}{4} }}{ (\dfrac{1}{3})^{-3} }$

(xᵃ)ᵇ = xᵃᵇ

xᵃ = 1/x⁻ᵃ

(a / b)ⁿ = aⁿ/bⁿ

aⁿ . bⁿ  = (ab)ⁿ

xᵃ . xᵇ = xᵃ⁺ᵇ

a⁰ = 1

27  = 3³

81 = 3⁴

$\dfrac{(3^3)^{-\frac{2}{3}} (3^4)^{\frac{5}{4} }}{ 3^3 }$

$\dfrac{(3)^{-2} (3^5)}{ 3^3 }$

$(3)^{-2+5-3}$

3⁰

= 1

$\dfrac{(27)^{-\frac{2}{3}} (81)^{\frac{5}{4} }}{ (\dfrac{1}{3})^{-3} }=1$

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