Question

the wnswer is 13.find the steps​

Answer 1

Solution :

$\longrightarrow \sf \: {( {2}^{2}) }^{0} + ({2})^{ - 4} \div ( {2})^{ - 6} + ( \dfrac{1}{2} ) ^{ - 3}$

$\longrightarrow \sf \: ({2})^{0} + (\dfrac{1}{2}) ^{4} \div (\dfrac{1}{2}) ^{6} + ({2})^{3}$

$\longrightarrow \sf \: 1 + \dfrac{1}{16} \div \dfrac{1}{64} + 8$

$\longrightarrow \sf \: 1 + \dfrac{1}{16} \times 64 + 8$

$\longrightarrow \sf \: 1 + 4 + 8$

$\longrightarrow \sf \large \boxed{ \purple{ \sf \: 13}}$

Required Value is 13

More about Exponents :

If a,b are positive real numbers and m,n are rational numbers,then :

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

$\bullet \sf \: {a}^{m} \div {a}^{n} = {a}^{m - n}$

$\bullet \sf \: ({a}^{m} )^{n} = {a}^{mn}$

$\bullet \sf \: {a}^{ - n} = \dfrac{1}{ {a}^{n} }$

$\bullet \sf \: ( {ab})^{n} = {a}^{n} {b}^{n}$

$\bullet \sf \: ( \dfrac{a}{b} ) ^{n} = \dfrac{ {a}^{n} }{ {b}^{n} }$

$\bullet \sf\: {a}^{0} = 1$

$\bullet \sf {a}^{-m} =( \dfrac{1}{a})^{m}$

Answer 2

Solution :-

$→( { {2}^{2}) }^{0} + {2}^{ - 4} \div {2}^{ - 6} + ( { \frac{1}{2}) }^{ - 3} \\ → ( {2 \times 2)}^{0} + ( { \frac{1}{2}) }^{4} \div ( { \frac{1}{2} )}^{6} + ( {2)}^{3} \\ → ( {4)}^{0} + \frac{1}{2 \times 2 \times 2 \times 2} \div \frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2} + (2 \times 2 \times 2)$

But -

• ${x}^{0} = 1$

$</strong><strong>→</strong><strong> 1 + \frac{1}{16} \div \frac{1}{64} + </strong><strong>8</strong><strong> \\ \\ </strong><strong>→</strong><strong> 1 + \frac{1}{16} \times 64 + </strong><strong>8</strong><strong> \\ \\ </strong><strong>→</strong><strong>1 + 4 + </strong><strong>8</strong><strong> \\ \\ </strong><strong>→</strong><strong>1</strong><strong>3</strong><strong>$

$\rule{200}{1}$

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