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Verified Answer :

Lampa20

numbers 27 and 81 have 27 as common factor which is equal to 3^3. Noting that we can put 27 before brackets write it in form 3^3 and that third root and cube will trim.

\(\sqrt[3]{27x - 81} - 5=\)
\(\sqrt[3]{27(x-3)} - 5 =\)
\(\sqrt[3]{3^3(x-3)} - 5=\)
\(3 \sqrt[3]{x-3} - 5\)

-5 means that graph is shifted 5 to down.
-3 means it is shifted to right by -3
3 and ∛ represent scaling of graph which can be seen and tested once you draw it. It is harder to explain it with words.

MrRoyal

The equivalent expression of \(\sqrt[3]{27x - 81} - 5\) is \(3 \sqrt[3]{(x - 3)} - 5\)

The expression is given as:

\(\sqrt[3]{27x - 81} - 5\)

Rewrite the expression, as an equation

\(y = \sqrt[3]{27x - 81} - 5\)

Factor out 27, from the radical expression

\(y = \sqrt[3]{27(x - 3)} - 5\)

Express 27 as the cube of 3

\(y = \sqrt[3]{3^3(x - 3)} - 5\)

Rewrite the radical expression, as a product

\(y = \sqrt[3]{3^3 * (x - 3)} - 5\)

Take the cube root of 3^3

\(y =3 \sqrt[3]{(x - 3)} - 5\)

Rewrite as:

\(3 \sqrt[3]{(x - 3)} - 5\)

Hence, the equivalent expression of \(\sqrt[3]{27x - 81} - 5\) is \(3 \sqrt[3]{(x - 3)} - 5\)

Read more about equivalent expressions at:

https://brainly.com/question/2972832

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