Let's break down and solve the given expression step by step:
[tex]\[
\sqrt[3]{(-9)(3)}(-2)^4 - \left(\sqrt{6^2}\right)(-3) + (-5)^0 + (-3)^2
\][/tex]
Step 1: Simplify inside the cubic root.
[tex]\[
(-9)(3) = -27
\][/tex]
So, we have:
[tex]\[
\sqrt[3]{-27}
\][/tex]
Step 2: Evaluate the cubic root.
[tex]\[
\sqrt[3]{-27} = -3
\][/tex]
So, the expression now becomes:
[tex]\[
(-3)(-2)^4 - \left(\sqrt{6^2}\right)(-3) + (-5)^0 + (-3)^2
\][/tex]
Step 3: Evaluate [tex]\((-2)^4\)[/tex].
[tex]\[
(-2)^4 = 16
\][/tex]
So, the expression now becomes:
[tex]\[
(-3)(16) - \left(\sqrt{6^2}\right)(-3) + (-5)^0 + (-3)^2
\][/tex]
Step 4: Multiply [tex]\((-3)\)[/tex] with [tex]\(16\)[/tex].
[tex]\[
(-3)(16) = -48
\][/tex]
So, the expression now becomes:
[tex]\[
-48 - \left(\sqrt{6^2}\right)(-3) + (-5)^0 + (-3)^2
\][/tex]
Step 5: Evaluate [tex]\(\sqrt{6^2}\)[/tex].
[tex]\[
\sqrt{6^2} = \sqrt{36} = 6
\][/tex]
So, the expression now becomes:
[tex]\[
-48 - (6)(-3) + (-5)^0 + (-3)^2
\][/tex]
Step 6: Multiply [tex]\(6\)[/tex] by [tex]\((-3)\)[/tex].
[tex]\[
6 \cdot (-3) = -18
\][/tex]
So, the expression now becomes:
[tex]\[
-48 - (-18) + (-5)^0 + (-3)^2
\][/tex]
Step 7: Evaluate [tex]\(-(-18)\)[/tex].
[tex]\[
-(-18) = 18
\][/tex]
So, the expression now becomes:
[tex]\[
-48 + 18 + (-5)^0 + (-3)^2
\][/tex]
Step 8: Evaluate [tex]\((-5)^0\)[/tex].
[tex]\[
(-5)^0 = 1
\][/tex]
So, the expression now becomes:
[tex]\[
-48 + 18 + 1 + (-3)^2
\][/tex]
Step 9: Evaluate [tex]\((-3)^2\)[/tex].
[tex]\[
(-3)^2 = 9
\][/tex]
So, the expression now becomes:
[tex]\[
-48 + 18 + 1 + 9
\][/tex]
Step 10: Combine the results.
Add these values together step-by-step:
[tex]\[
-48 + 18 = -30
\][/tex]
[tex]\[
-30 + 1 = -29
\][/tex]
[tex]\[
-29 + 9 = -20
\][/tex]
Thus, the value of the expression is:
[tex]\[
-20
\][/tex]
