Step 1a

Rewrite the expression.

Explanation: Rewrite the expression,

\$(4x^3)(3y^2)(2x^2y^(-2))\$ as

\$(4x^3)(3y^2)(2x^2)/y^2\$.

Step 1b

Evaluate the exponents.

Explanation: Evaluate the exponents by using law of exponents

\$ 4(x^3)2(x^2)((3y^2)/y^2)\$

⇒ \$4(2)(x^(3 + 2))(3y^(2-2))\$

⇒ \$4(2)(x^(5))(3y^(0))\$

⇒ \$4(2)(x^(5))(3(1))\$ ∵ \$a^0 = 1\$

Step 1c

Perform multiplication among the terms.

Explanation: Operate multiplication among the terms in the expression obtained afer evaluating the exponents.

⇒ \$4(2)(x^(5))(3(1))\$

⇒ \$8(x^(5))3\$

⇒ \$24(x^5)\$

⇒ \$24x^5\$

∴ \$(4x^3)(3y^2)(2x^2y^(-2)) = 24x^5\$.