Question

(3⁵×10⁵×25)÷(5⁷×6⁵) Simplify
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Answer 1

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( 3⁵ × 10⁵ × 25 ) ÷ ( 5⁷ × 6⁵ )

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$= \bf{\frac{3⁵\:×\:10⁵\:×\:25}{5⁷\:×\:6⁵}} \\ \\ = \bf{\frac{3⁵\:×\:(2\:×\:5)⁵\:×\:5²}{5⁷\:×\:(2\:×\:3)⁵}} \\ \\ \bf{\frac{3⁵\:×\:2⁵\:×\:5⁵\:×\:5²}{5^{5-2}\:×\:2⁵\:×\:3⁵}} \\ \\ = \bf{\frac{3^{5-5}\:×\:2^{5-5}\:×\:5^{5-5}\:×\:5²}{5²}} \\ \\ = \bf{3⁰\:×\:2⁰\:×\:5⁰\:×\:5^{2-2}} \\ \\ = \bf{1 \times 1 \times 1 \times 5^{0}} \\ \\ = \bf{1\:×\:1\:×\:1\:×\:1} \\ \\ = \bf{1}$

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Give a look here :-

• multiplication of two numbers of same exponents results in the addition of their powers . example -
• $a^{m} \times a^{n} \:=\: a^{m+n}$
• division of two numbers of same exponents results in the subtraction of their powers . example -
• $\bf{\frac{a^{m}}{a^{n}}} \:=\: a^{m-n}$

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Answer 2

..Question..ㅤ

( 3⁵ × 10⁵ × 25 ) ÷ ( 5⁷ × 6⁵ )

..Answer..

$= \bf{\frac{3⁵\:×\:10⁵\:×\:25}{5⁷\:×\:6⁵}} \\ \\ = \bf{\frac{3⁵\:×\:(2\:×\:5)⁵\:×\:5²}{5⁷\:×\:(2\:×\:3)⁵}} \\ \\ \bf{\frac{3⁵\:×\:2⁵\:×\:5⁵\:×\:5²}{5^{5-2}\:×\:2⁵\:×\:3⁵}} \\ \\ = \bf{\frac{3^{5-5}\:×\:2^{5-5}\:×\:5^{5-5}\:×\:5²}{5²}} \\ \\ = \bf{3⁰\:×\:2⁰\:×\:5⁰\:×\:5^{2-2}} \\ \\ = \bf{1 \times 1 \times 1 \times 5^{0}} \\ \\ = \bf{1\:×\:1\:×\:1\:×\:1} \\ \\ = \bf{1}$

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Give a look here :-

• multiplication of two numbers of same exponents results in the addition of their powers . example -
• $a^{m} \times a^{n} \:=\: a^{m+n}$
• division of two numbers of same exponents results in the subtraction of their powers . example -
• $\bf{\frac{a^{m}}{a^{n}}} \:=\: a^{m-n}$

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