Question

Which expression is equivalent to ^3 27x^18?
A. 3x3
B. 3x6
C. 9x3
D. 9x6

Answer 1

∛27x^18 =
=∛(3x^6)^3
= 3x^6

answer
B. 3x^6

Answer 2

Option (b) is correct.

The Equivalent expression to given expression
`\sqrt[3]{27x^(18)}` is
`3x^6`

Explanation:

Given : Expression
`\sqrt[3]{27x^(18)}`

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

Consider the given expression
`\sqrt[3]{27x^(18)}`

Can be written as
`\left(27x^(18)\right)^{(1)/(3)}`

Apply exponent rule
`\left(a\cdot \:b\right)^n=a^nb^n`

We have,

`=27^{(1)/(3)}\left(x^(18)\right)^{(1)/(3)}`

Factor 27 as
`\:27=3^3`

`\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^(bc)`

we have,

`\left(3^3\right)^{(1)/(3)}=3^{3\cdot (1)/(3)}=3`

Also, For
`\left(x^(18)\right)^{(1)/(3)}`

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

`=x^6`

Thus,
`\left(27x^(18)\right)^{(1)/(3)}=3x^6`

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