lostintranslation123
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someone help meh pleasee

Someone Help Meh Pleasee class=

Sagot :

The answer is  [tex]\mathsf {\frac{2}{9}}[/tex].

We are given the equation :

  • ∛(8/729)
  • ∛8/∛729
  • 2/9
semsee45

Answer:

[tex]\dfrac{2}{9}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[3]{\dfrac{8}{729}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \left(\dfrac{8}{729}\right)^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]

[tex]\implies \dfrac{8^{\frac{1}{3}}}{729^{\frac{1}{3}}}[/tex]

Rewrite 8 as (2 · 2 · 2) and rewrite 729 as (9 · 9 · 9):

[tex]\implies \dfrac{(2 \cdot 2 \cdot 2)^{\frac{1}{3}}}{(9 \cdot 9 \cdot 9)^{\frac{1}{3}}}[/tex]

[tex]\implies \dfrac{(2^3)^{\frac{1}{3}}}{(9^3)^{\frac{1}{3}}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{2^{(3 \cdot \frac{1}{3})}}{9^{(3 \cdot \frac{1}{3})}}[/tex]

[tex]\implies \dfrac{2^1}{9^1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]

[tex]\implies \dfrac{2}{9}[/tex]

Learn more about exponent rules here:

https://brainly.com/question/27959936

https://brainly.com/question/27953406

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