(1) Simplified expression: [tex]4 x^{2}[/tex]
(2) Simplified expression: [tex]-343 x^{3}[/tex]
(3) Simplified expression: [tex]45 x^{24}[/tex]
(4) Simplified expression: [tex]36x^{2}[/tex]
Solution:
(1) Original expression: [tex](2 x)^{2}[/tex]
[tex](2 x)^{2}=2^2x^2=4x^2[/tex]
Simplified expression: [tex]4 x^{2}[/tex]
(2) Original expression: [tex](-7 x)^{3}[/tex]
[tex](-7 x)^{3}=(-7)^3 x^3=-343x^3[/tex]
Simplified expression: [tex]-343 x^{3}[/tex]
(3) Original expression: [tex]5 x^{9} \cdot 3 x^{8} \cdot 3 x^{7}[/tex]
Multiply the numerical coefficients.
[tex](5\cdot 3\cdot 3) x^{9} \cdot x^{8} \cdot x^{7}[/tex]
If the bases are equal then the powers can add.
[tex]45 x^{9+8+7}[/tex]
[tex]45 x^{24}[/tex]
Simplified expression: [tex]45 x^{24}[/tex]
(4) Original expression: [tex]4(3 x)^{2}[/tex]
[tex]4(3 x)^{2} =4 (3^2x^2)[/tex]
[tex]=4\left(9 x^{2}\right)[/tex]
[tex]=36x^{2}[/tex]
Simplified expression: [tex]36x^{2}[/tex]
