We will make use of the following properties : ⇒ a^m× a^n=a^m+n.......[ 1] #160; #160; #160; a^m÷ a^n=a^m n.......[ 2] using these we can simpl ...

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Standard IX

Mathematics

Quotient Law

Simplify 52...

Question

Simplify $(5^{2} \times 5^{4}) \div 5^{3}$ .

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Solution

We will make use of the following properties :
$\Rightarrow a^{m} \times a^{n} = a^{m + n} . . . . . . . [1]$
$a^{m} \div a^{n} = a^{m - n} . . . . . . . [2]$
using these we can simplify
$(5^{4} \times 5^{2}) \div 5^{3}$
$= 5^{4 + 2} \div 5^{3}$
$= 5^{6} \div 5^{3}$
$= 5^{6 - 3}$
$= 5^{3}$
$= 125$
Hence, the answer is $125.$

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Similar questions

Q. Simplify.

(i)

5^{4} \times 5^{3}

(ii)

{(\frac{2}{3})}^{6} \div {(\frac{2}{3})}^{9}

(iii)

{(\frac{7}{2})}^{8} \times {(\frac{7}{2})}^{- 6}

(iv)

{(\frac{4}{5})}^{2} \div (\frac{5}{4})

Q. Simplify:

5^{4} \div 5^{3}

Q. Simplify

5^{2} \times 5^{3}

Question 84 (e)

Simplify and express each of the following in exponential form.
$[{(\frac{3}{5})}^{3} \times {(\frac{3}{5})}^{8}] \div [{(\frac{3}{5})}^{2} \times {(\frac{3}{5})}^{4}]$

Q. Simplify:

\frac{2^{3} \times 3^{2} \times 5^{4}}{3^{3} \times 5^{2} \times 2^{4}}

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Simplify (52×54)÷53.

We will make use of the following properties :⇒am×an=am+n.......[1] am÷an=am−n.......[2]using these we can simplify (54×52)÷53=54+2÷53=56÷53=56−3=53=125Hence, the answer is 125.

Simplify $(5^{2} \times 5^{4}) \div 5^{3}$ .