2.0*10^-19 = x(3x)^3
solve for x and show working
To solve for x in the equation 2.0*10^-19 = x(3x)^3, we can follow these steps:
Step 1: Simplify the equation.
(3x)^3 can be further simplified as 27x^3 by raising the 3x to the power of 3.
So the equation becomes:
2.0*10^-19 = 27x^3
Step 2: Isolate the term with x.
To isolate x, divide both sides of the equation by 27:
(2.0*10^-19)/27 = (27x^3)/27
Simplify:
7.40740741 * 10^-21 = x^3
Step 3: Take the cube root of both sides.
Taking the cube root of both sides will allow us to solve for x:
∛(7.40740741 * 10^-21) = ∛(x^3)
Simplify:
∛(7.40740741) * ∛(10^-21) = x
Step 4: Evaluate the cube root and simplify.
Using a calculator, the cube root of 7.40740741 is approximately 1.92.
The cube root of 10^-21 is 0.1, since 10^-21 can be written as (10^-3)^7 = (0.001)^7 = 0.000000000000001.
So, x ≈ 1.92 * 0.1
Simplifying the expression:
x ≈ 0.192
Therefore, x is approximately 0.192.