It took me a little while to understand what you're trying to do. At first I thought you were trying to solve the equation above. Then I realized that the goal was to simplify the expression on the left side, above.umzung said:$$10π \left( \frac V {4π} \right)^{2/3} = 5\sqrt[3] {{V^2}\frac π 2}$$
One thing to realize is that ##(a)^{\frac 2 3}## is equal to ##(a^2)^{\frac 1 3}##. Can you start simplifying based on this hint?umzung said:Not sure how to deal with the ##10π## and how we get ##\frac π 2##.
Fractional indices, also known as rational exponents, are a way of representing powers or roots of numbers that are not whole numbers. They are written in the form of a fraction, with the numerator representing the power and the denominator representing the root.
To simplify a fractional index, you can use the following rules:
Sure, for example, if we have the fractional index 27^(2/3), we can rewrite it as the cube root of 27 squared. The cube root of 27 is 3, so the simplified form is 3^2, which equals 9.
Some common mistakes include forgetting to simplify the fraction before applying the rules, mixing up the numerator and denominator, and not recognizing when the index can be rewritten as a power or root.
Fractional indices are used in various fields of science and engineering, such as physics, chemistry, and computer science. They are also used in finance and economics to calculate compound interest and growth rates. In everyday life, fractional indices can be used to solve mathematical problems and simplify complex calculations.