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What is the simplified form of (2/3)^3


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Sagot :

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.

Solution:-

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.

________________________________

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]