Question

(8^2 ÷ 8^-7)^2 ÷ (64 x 2^3)​

Answer 1

$\dfrac{( {8}^{2} \div {8}^{ - 7})^{2} }{64 \times {2}^{3} }$

${a}^{m} \div {a}^{m} = {a}^{m - n}$

by expressing 64 as 2⁶

$\dfrac{( {8}^{2 - ( - 7)})^{2} }{ {2}^{6} \times {2}^{3} }$

$\dfrac{ { ({8}^{9} })^{2} }{ {2}^{6} \times {2}^{3} }$

${a}^{m} \times {a}^{n} = { a}^{m + n}$

${ ({a}^{n}) }^{m} = {a}^{mn}$

$\dfrac{ {8}^{18} }{ {2}^{9} }$

by expressing 8¹⁸ as (2³)¹⁸

$\dfrac{ ({2}^{3})^{18} }{ {2}^{9} }$

$({a}^{n})^{n} = {a}^{mn}$

$\dfrac{ {2}^{36} }{ {2}^{9} }$

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

${2}^{36 - 9} = {2}^{27}$

Answer =≥ 134,217,728

Important points to note :

${a}^{m} \times {a}^{n} = {a}^{m + n}$

${a}^{n} \times {b}^{n} = {ab}^{n}$

${a}^{m} \div {a}^{n} = {a}^{m - n}$

${a}^{m} \div {b}^{m} = ( \frac{a}{b})^{m}$

${a}^{ - m} = \frac{1}{ {a}^{m} }$

a⁰ = 1

a¹ = a.

Answer 2

Question:

$\frac{(8 \ {}^{2} \div 8) {}^{ - 7} }{64 \times 2 {}^{3} }$

☆Using -

$a {}^{m} - a {}^{n} = a {}^{m - n}$

here, 64 can be written as 2⁶.

$➪ \: ( \frac{8 {}^{2 - ( - 7)} }{2 {}^{6} \times 2 {3}^{2} } {)}^{2}$

$➪ \: \frac{(8 {}^{9) {}^{2} } }{2 {}^{6} \times 2 {}^{3} }$

$➪ \: a {}^{m} \times a {}^{n} = a {}^{m + n}$

$➪ \: (a {}^{m} ) {}^{n} = a {}^{mn}$

$= \frac{8 {}^{18} }{2 {}^{9} }$

By Expressing 8¹⁸ as (2³)¹⁸.

$\frac{(2 {}^{3}) {}^{18} }{2 {}^{9} }$

$➪ \: (a {}^{m} ) {}^{n} = a {}^{mn}$

$= \frac{2 {}^{36} }{2 {}^{9} }$

$\frac{a {}^{m} }{a {}^{n} } = a {}^{m - n}$

$➪ \: 2 {}^{36 - 9} = 2 {}^{27}$

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