Question

What is the value of $x$ for
$(3^3{)}^2\times (2^3{)}^2=x^6$?

• A. $6$
• B. $4$
• C. $9$
• D. $8$

Answer 1

The correct option is A $6$

Given:
$(3^3{)}^2\times (2^3{)}^2=x^6$
Let us first solve $(3^3{)}^2\times (2^3{)}^2$
$(3^3{)}^2\times (2^3{)}^2=(3^3\times 2^3{)}^2$
$[\because a^m\times b^m=(a\times b{)}^m]$
$={\left(\right(3\times 2{)}^3)}^2$
$=(6^3{)}^2$
$=6^{3\times 2}$
$=6^6$
Note: Do not write $(3^3{)}^2$ and $(2^3{)}^2$ as $3^{\left(3^2\right)}$ and $2^{\left(3^2\right)}$, respectively.
$3^{\left(3^2\right)}\times 2^{\left(3^2\right)}=3^9\times 2^9=6^9$,which is incorrect.

$\Rightarrow (3^3{)}^2\times (2^3{)}^2=6^6=x^6$

Thus, $x=6$