Simplify ab2c3- a4b5c-6-a-7b-8c9 - a10b11c-12- a13b-14c15

Ab^2c^3× a^4b^5c^ 6/a^ 7b^ 8c^9 × a^10b^11c^ 12× a^13b^ 14c^15 ∵ a^m × a^n=a^m+n ⇒a^5b^7c^ 3/a^3b^3c^ 3× nbsp;a^13b^ 14c^15 ⇒a^5b^7c^ 3/a^16b^ 11c^12 ∵a^m ...

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Byju's Answer

Standard IX

Mathematics

Quotient Law

Simplify ab2c...

Question

Simplify $\frac{a b^{2} c^{3} \times a^{4} b^{5} c^{- 6}}{a^{- 7} b^{- 8} c^{9} \times a^{10} b^{11} c^{- 12} \times a^{13} b^{- 14} c^{15}}$

a^{11} b^{18} c^{- 15}

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a^{11} b^{18} c^{15}

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a^{- 11} b^{- 18} c^{15}

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a^{- 11} b^{18} c^{- 15}

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Solution

The correct option is D $a^{- 11} b^{18} c^{- 15}$
$\frac{a b^{2} c^{3} \times a^{4} b^{5} c^{- 6}}{a^{- 7} b^{- 8} c^{9} \times a^{10} b^{11} c^{- 12} \times a^{13} b^{- 14} c^{15}}$

$∵ a^{m} \times a^{n} = a^{m + n}$

$\Rightarrow \frac{a^{5} b^{7} c^{- 3}}{a^{3} b^{3} c^{- 3} \times a^{13} b^{- 14} c^{15}}$

$\Rightarrow \frac{a^{5} b^{7} c^{- 3}}{a^{16} b^{- 11} c^{12}}$

$∵ \frac{a^{m}}{a^{n}} = a^{m - n}$

$\Rightarrow a^{(5 - 16)} b^{(7 + 11)} c^{(- 3 - 12)}$

$\Rightarrow a^{- 11} b^{18} c^{- 15}$

Suggest Corrections

Simplify ab2c3×a4b5c−6a−7b−8c9×a10b11c−12×a13b−14c15

The correct option is D a−11b18c−15ab2c3×a4b5c−6a−7b−8c9×a10b11c−12×a13b−14c15 ∵am×an=am+n ⇒a5b7c−3a3b3c−3×a13b−14c15 ⇒a5b7c−3a16b−11c12 ∵aman=am−n ⇒a(5−16)b(7+11)c(−3−12) ⇒a−11b18c−15

Simplify $\frac{a b^{2} c^{3} \times a^{4} b^{5} c^{- 6}}{a^{- 7} b^{- 8} c^{9} \times a^{10} b^{11} c^{- 12} \times a^{13} b^{- 14} c^{15}}$