Question 180vSimplify93 - 27 - t4-3-2- 34 - t2

(9)^3 × 27 × t^4/(3)^ 2× (3)^4 × t^2 = (3^2)^3 × (3)^3 × t^4/(3)^ 2× (3)^4 × t^2 [∵ 3 × 3 = 3^2 = 9] =(3)^6 × (3)^3 × t^4/(3)^ 2× (3)^4 × t^2 = (3)^6 ...

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Byju's Answer

Standard IX

Mathematics

Product Law

Question 180v...

Question

Question 180(v)

Simplify

$\frac{(9)^{3} \times 27 \times t^{4}}{(3)^{- 2} \times (3)^{4} \times t^{2}}$

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Solution

$\frac{(9)^{3} \times 27 \times t^{4}}{(3)^{- 2} \times (3)^{4} \times t^{2}} = \frac{(3^{2})^{3} \times (3)^{3} \times t^{4}}{(3)^{- 2} \times (3)^{4} \times t^{2}} [∵ 3 \times 3 = 3^{2} = 9]$
$= \frac{(3)^{6} \times (3)^{3} \times t^{4}}{(3)^{- 2} \times (3)^{4} \times t^{2}}$
$= (3)^{6} \times (3)^{3} \times (3)^{2} \times (3)^{- 4} \times t^{4} \times t^{- 2} [∵ a^{- m} = \frac{1}{a^{m}}]$
$= (3)^{6 + 3 + 2 + (- 4)} \times t^{4 + (- 2)} [∵ a^{m} \times a^{n} = (a)^{m + n}]$

$= 3^{11 - 4} \times t^{4 - 2}$

$= 3^{7} \times t^{2}$

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Question 180(v) Simplify (9)3×27×t4(3)−2×(3)4×t2

(9)3×27×t4(3)−2×(3)4×t2=(32)3×(3)3×t4(3)−2×(3)4×t2 [∵3×3=32=9] =(3)6×(3)3×t4(3)−2×(3)4×t2 =(3)6×(3)3×(3)2×(3)−4×t4×t−2 [∵a−m=1am] =(3)6+3+2+(−4)×t4+(−2) [∵am×an=(a)m+n] =311−4×t4−2 =37×t2

Question 180(v)

Simplify

$\frac{(9)^{3} \times 27 \times t^{4}}{(3)^{- 2} \times (3)^{4} \times t^{2}}$