Multiply the following radical expression: \$root(3) (8x^6) times root(3) (27x^9)\$.

Given expression

\$root(3) (8x^6) times root(3) (27x^9)\$

Express each term under a single cube root:

\$root(3) (8x^6) \times root(3) (27x^9) = root(3)((8x^6) times (27x^9))\$

Multiply the terms inside the cube root:

\$(8x^6) times (27x^9) = (8 \times 27) \times (x^6 \times x^9)\$

\$216x^(6+9) = 216x^15\$

Simplify inside the cube root:

\$root(3)(216x^15)\$

Recognize that 216 is a perfect cube (since 216 = \$6^3\$):

216 = \$6^3\$

Simplify the cube root of each part:

\$root(3)(6^3 x^15) = 6 x^(15/3) = 6 x^5\$

Therefore, the simplified expression is \$6x^5\$.

This option is incorrect because it suggests a simpler result than \$6x^5\$, which is the correct simplified form of the expression

\$2x^5\$

This option does not match the simplified result \$6x^5\$. It suggests a higher coefficient and does not reflect the correct multiplication of the radicals

\$12x^5\$

This option is not correct because it introduces a negative sign, which is not present in the simplified expression \$6x^5\$

\$-12x^5\$

This option accurately represents the simplified result of the multiplication of the cube roots \$root(3)(8x^6) \times root(3)(27x^9)\$, which simplifies to \$6x^5\$

\$6x^5\$

Option

D

Can you summarize what you’ve understood in the above steps?