Middle School

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Which expression is equivalent to [tex] \sqrt[3]{27x^{18}}[/tex]?

A. [tex] 3x^{3} [/tex]

B. [tex] 3x^{6} [/tex]

C. [tex] 9x^{3} [/tex]

D. [tex] 9x^{6} [/tex]

Answer :

Answer:

Option (b) is correct.

The Equivalent expression to given expression [tex]\sqrt[3]{27x^{18}}[/tex] is [tex]3x^6[/tex]

Step-by-step explanation:

Given : Expression [tex]\sqrt[3]{27x^{18}}[/tex]

We have to choose an equivalent expression to the given expression [tex]\sqrt[3]{27x^{18}}[/tex]

Consider the given expression [tex]\sqrt[3]{27x^{18}}[/tex]

Can be written as [tex]\left(27x^{18}\right)^{\frac{1}{3}}[/tex]

Apply exponent rule [tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]

We have,

[tex]=27^{\frac{1}{3}}\left(x^{18}\right)^{\frac{1}{3}}[/tex]

Factor 27 as [tex]\:27=3^3[/tex]

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

we have,

[tex]\left(3^3\right)^{\frac{1}{3}}=3^{3\cdot \frac{1}{3}}=3[/tex]

Also, For [tex]\left(x^{18}\right)^{\frac{1}{3}}[/tex]

[tex]\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]

[tex]=x^6[/tex]

Thus, [tex]\left(27x^{18}\right)^{\frac{1}{3}}=3x^6[/tex]

Thus, The Equivalent expression to given expression [tex]\sqrt[3]{27x^{18}}[/tex] is [tex]3x^6[/tex]

Thanks for taking the time to read Which expression is equivalent to tex sqrt 3 27x 18 tex A tex 3x 3 tex B tex 3x 6 tex C tex 9x 3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

∛27x^18 =
=∛(3x^6)^3
= 3x^6

answer
B. 3x^6