Question

Consider the statement square root 300c^9 = 10c^x square root 3 c

Answer 1

Answer:

Given the statement: Square root 300c^9 = 10c^x square root 3 c

⇒$\sqrt{300c^9} =10c^x\sqrt{3c}$

Squaring both sides we get;

$(\sqrt{300c^9})^2= (10c^x\sqrt{3c})^2$

Simplify:

$300c^9 = 100c^{2x}(3c)$

We know: $a^m \cdot a^n = a^{m+n}$

then;

$300c^9 = 300c^{2x+1}$

Divide both sides by 300 we get;

$c^9 = c^{2x+1}$

On comparing both sides we have;

$9 = 2x+1$

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.