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Answer:
[tex]\boxed{\tt \cfrac{8}{27} }[/tex]
OR,
[tex]\boxed{\tt ≈\: 0.296}[/tex]
Step-by-step explanation:
Given arithmetic expression:-
[tex] \bigg({ \cfrac{2}{3} } \bigg)^{3} [/tex]
We need to find the simplified form of the given arithmetic expression.
In words, the question may be represented as 2/3 raised to the power of 3.
[tex] \sf \implies\bigg({ \cfrac{2}{3} } \bigg)^{3} [/tex]
[tex]\sf \implies \: \bigg( {\cfrac{2}{3} \bigg) }^{} \times \bigg( {\cfrac{2}{3} \bigg) }^{} \times \bigg( {\cfrac{2}{3} \bigg) }^{}[/tex]
It Can be rewritten as,
[tex]\sf \implies \cfrac{2 \times 2 \times 2}{3 \times 3 \times 3} [/tex]
Multiply it :-
[tex]\sf \implies \cfrac{4\times 2}{9\times 3} [/tex]
[tex]\sf \implies \: \cfrac{8}{27} [/tex]
In Decimal:-
[tex]\sf\implies\: 0.296[/tex]
Hence, the simplest form of the arithmetic expression [exponent] is 8/27.
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I hope this helps!
Let me know if you have any questions.
[tex] = > ( \frac{2}{3} {)}^{3} [/tex]
[tex] = > ( \frac{2}{3} \times \frac{2}{3 } \times \frac{2}{3} )[/tex]
[tex] = > ( \frac{2 \times 2 \times 2}{3 \times 3 \times 3} )[/tex]
[tex] = > \frac{2 \times 2 \times 2}{3 \times 3 \times 3} [/tex]
[tex] = > \frac{8}{27} [/tex]