Question

Simplify and write tye answer in exponential form
$\huge \sf \color{lime} (2^5 ÷ 2^8 ) × 2^-5$
Please solve the number ⬆️


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@Fiza100 @Sk2 ​

Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt Simplify\: and \:write\: the\: answer\: in\: exponential\: form$

$\bf \Big({2}^{5} \div {2}^{8}\Big) \times {2}^{-5}$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf \implies \Big({2}^{5} \div {2}^{8}\Big) \times {2}^{-5}$

$\sf \bf \implies \bigg(\dfrac{{2}^{5}}{{2}^{8}}\bigg) \times {2}^{-5}$

${\color {blue} {\boxed {\boxed {\boxed {\sf Using \: \: \dfrac{{a}^{m}}{{a}^{n}} = {a}^{m-n}}}}}}$

$\sf \bf \implies \Big({2}^{5-8}\Big) \times {2}^{-5}$

$\sf \bf \implies {2}^{-3} \times {2}^{-5}$

${\color {blue} {\boxed {\boxed {\boxed {\sf Using \: \: {a}^{m}\times {a}^{n}= {a}^{m+n}}}}}}$

$\sf \bf \implies {2}^{-3+ \big(-5 \big)}$

$\sf \bf \implies {2}^{-3-5}$

$\sf \bf \implies {2}^{-8}$

${\color {blue} {\boxed {\boxed {\boxed {\sf Using \: \: \bf {a}^{-m} =\dfrac{1}{{a}^{m}}}}}}}$

$\implies {\boxed {\boxed {\color {aqua} {\sf \bf \dfrac{1}{{2}^{8}}}}}}$

${\underbrace {\color {red} {\overline {\color {red} {\underline {\color {red} {\sf \therefore The\:exponential\:form \:of \:\Big({2}^{5} \div {2}^{8}\Big) \times {2}^{-5}\:is\:\dfrac{1}{{2}^{8}}}}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

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$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

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

$\bf \dfrac{{a}^{m}}{{a}^{n}} ={a}^{m-n}$

$\bf \big({a}^{m}\big)^{n} ={a}^{mn}$

$\bf {a}^{-m} =\dfrac{1}{{a}^{m}}$

$\bf {a}^{m} \times {b}^{m} ={ab}^{m}$