Question

Find the value of (1/2)4÷(1/3)4+(1/2)3​

Answer 1

Correct Question :

›»› Find the value of (1/2)⁴ ÷ (1/3)⁴ + (1/2)³

Answer :

›»› The value is 5.1875

Given :

• (1/2)⁴ ÷ (1/3)⁴ + (1/2)³

To Find :

• The value (1/2)⁴ ÷ (1/3)⁴ + (1/2)³ = ?

Solution :

$\tt{:\implies {\bigg(\dfrac{1}{2} \bigg)}^{4} \div {\bigg( \dfrac{1}{3} \bigg)}^{4} + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{:\implies \dfrac{{1}^{4}}{{2}^{4}} }\div {{\bigg( \dfrac{1}{3} \bigg)}^{4} + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{:\implies \dfrac{1}{{2}^{4}} }\div {{\bigg( \dfrac{1}{3} \bigg)}^{4} + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{:\implies \dfrac{1}{16} }\div {{\bigg( \dfrac{1}{3} \bigg)}^{4} + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{: \implies \dfrac{1}{16} \div \dfrac{ {1}^{4} }{ {3}^{4} } + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{: \implies \dfrac{1}{16} \div \dfrac{1}{ {3}^{4} } + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{: \implies \dfrac{1}{16} \div \dfrac{1}{81} + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{: \implies \dfrac{1}{16} \div \dfrac{1}{81} + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{: \implies \dfrac{1}{16} \times \dfrac{81}{1} + {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{: \implies \dfrac{81}{16}+ {\bigg( \dfrac{1}{2} \bigg)}^{3}}$

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$\tt{: \implies \dfrac{81}{16} + \dfrac{ {1}^{3} }{ {2}^{3} } }$

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$\tt{: \implies \dfrac{81}{16} + \dfrac{1}{ {2}^{3} } }$

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$\tt{: \implies \dfrac{81}{16} + \dfrac{1}{8} }$

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$\tt{: \implies \dfrac{81}{16} + \dfrac{1 \times 2}{8 \times 2} }$

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$\tt{: \implies \dfrac{81}{16} + \dfrac{2}{16} }$

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$\tt{: \implies \dfrac{81}{16} + \dfrac{2}{16} }$

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$\tt{: \implies \dfrac{81 + 2}{16} }$

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$\tt{: \implies \dfrac{83}{16}}$

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$\frak{: \implies \underline{ \boxed{ \pink{ \frak{5.1875}}}}}$

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║Hence, the value is 5.187.║