Match the following columns using multiplication rule of exponent.

5^{- 7}

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7^{- 2}

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3^{6}

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Solution

Note: $a^{m} \times a^{n} = a^{m + n}$
So,
$∙ 3^{4} \times 3^{2}$
$= 3^{(4 + 2)}$
$= 3^{6}$

$∙ 7^{- 3} \times 7^{1}$
$= 7^{(- 3 + 1)}$
$= 7^{- 2}$

$∙ 5^{- 4} \times 5^{- 3}$
$= 5^{(- 4 - 3)}$
$= 5^{- 7}$

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Similar questions

Sr. No.	Form of Exponent	Repeated multiplication	Result
1)	$a^{2} \times a^{3}$	....................	$a^{2 + 3} = a^{5}$
2)	$2^{5} \div 2^{3}$	.....................	$2^{2} = 4$
3)	....................	$\frac{x \times x \times x}{x \times x \times x \times x}$	$\frac{1}{x}$
4)	$(_{2})^{3} \div (- 2)^{3}$	$\frac{(- 2) \times (- 2) \times (- 2)}{(- 2) \times (- 2) \times (- 2)}$	....................
5)	$(m^{2})^{3}$	$m^{2} \times m^{2} \times m^{2}$	....................
6)	....................	$2 x \times 2 x \times 2 x$	$2^{3} \times x^{3}$
7)	${(\frac{7}{b})}^{3}$	....................	$\frac{7^{3}}{b^{3}}$

(a b)^{n} = a^{n} b^{n}

[7^{8} \times 12^{8}] \div [14^{8} \times 6^{8}]

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