Question

Simplify: (1/9)-½×(64)-⅓​

Answer 1

Answer:

$12 \sqrt[3]{4}$

Step-by-step explanation:

${ \frac{1}{9} }^{ - \frac {1}{2} } \: \times {64}^{ - \frac{1}{3} } \\ = ) { 9 }^{ \frac{1}{2} } \times { \frac{1}{64} }^{ \frac{1}{3} } \\ = ) \sqrt{9 } \times \sqrt[3]{64} \\ = ) \: 3 \times 4 \sqrt[3]{4 } \\ = ) 12\sqrt[3]{4}$

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Answer 2

Given:-

$\implies \tt \dfrac{1}{9}^{-\dfrac{1}{2}} \times (64)^{-\dfrac{1}{3}}$

Solution:-

$\implies \tt \bigg(\dfrac{1}{9}\bigg)^{-\dfrac{1}{2}} \times (64)^{-\dfrac{1}{3}}$

$\implies \tt \bigg(\dfrac{1}{3}\bigg)^{2}\times^{(\dfrac{-1}{2})} \times(4)^{3}\times^{(\dfrac{-1}{3})} \\ \\ \\ \implies \tt \bigg(\dfrac{1}{3}\bigg)^{-1} \times (4)^{-1} \\ \\ \\ \implies \tt 3 \times \dfrac{1}{4} \\ \\ \\ \implies \tt \dfrac{3}{4}$

Note:-

• $\dfrac{1}{9}$ can be written as $\bigg(\dfrac{1}{3}\bigg)^{2}$
• 64 can be written as (4)³.
• From this note no confusion arises.

Answer:-

$\large {\boxed {\boxed {\sf{\red {\dfrac{3}{4} }}}}}$

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