Answer:
Given the statement: Square root 300c^9 = 10c^x square root 3 c
⇒\sqrt{300c^9} =10c^x\sqrt{3c}
300c
9
=10c
x
3c
Squaring both sides we get;
(\sqrt{300c^9})^2= (10c^x\sqrt{3c})^2(
300c
9
)
2
=(10c
x
3c
)
2
Simplify:
300c^9 = 100c^{2x}(3c)300c
9
=100c
2x
(3c)
We know: a^m \cdot a^n = a^{m+n}a
m
⋅a
n
=a
m+n
then;
300c^9 = 300c^{2x+1}300c
9
=300c
2x+1
Divide both sides by 300 we get;
c^9 = c^{2x+1}c
9
=c
2x+1
On comparing both sides we have;
9 = 2x+19=2x+1
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.
