Answer:
Given the statement: Square root 300c^9 = 10c^x square root 3 c
⇒[tex]\sqrt{300c^9} =10c^x\sqrt{3c}[/tex]
Squaring both sides we get;
[tex](\sqrt{300c^9})^2= (10c^x\sqrt{3c})^2[/tex]
Simplify:
[tex]300c^9 = 100c^{2x}(3c)[/tex]
We know: [tex]a^m \cdot a^n = a^{m+n}[/tex]
then;
[tex]300c^9 = 300c^{2x+1}[/tex]
Divide both sides by 300 we get;
[tex]c^9 = c^{2x+1}[/tex]
On comparing both sides we have;
[tex]9 = 2x+1[/tex]
Subtract 1 from both sides we get;
8 = 2x
Divide both sides by 2 we have;
x = 4
Therefore, for the value of x =4 the given statement is true.
