Question 230622
{{{x^0.725 = 41.494}}}
Since the goal is to have an equation that says:
x = some number
Since the exponent on x is 1, we can look at the problem as: "How do I change an exponent of 0.725 to a 1?" One way we could do this is to raise both sides to the 1/0.725 power. Let's see:
{{{(x^0.725)^(1/0.725) = (41.494)^(1/0.725)}}}
The left side works out to be x because<ul><li>{{{(a^b)^c = a^(bc)}}}</li><li>0.725 and 1/0.725 are reciprocals</li><li>When you multiply reciprocals you always get 1</li><li>{{{x^1 = x}}}</li></ul>
So we have
{{{x = (41.494)^(1/0.725)}}}
We can use our calculators to find the right side. (It works out to be approximately 170.4919451462086020.)