# Negative & Fractional Indices

## Negative Indices

Example 1 In this example, we simply flipped the fraction around which allowed us to make the exponent positive so that we can easily find the answer.
Example 2 In example 2, we also simply used the reciprocal and then solved the expression with the positive exponent.
Example 1 In example 1: we have to square root 16 and then cube our solution to get the answer: 64.
Example 2 In example, 2, we have to find the cube root instead of the square root. The general procedure remains the same.
Example 3 In the last example we have to find the fourth root. We can see this by looking at the bottom number of the fractional exponent.
Example 1 In example 1, we start off by taking the reciprocal and square rooting 9. Then we cube the answer and get 1/27 as the final solution.
Example 2 In example 2, we do the same procedure as in example one just that we cube root and square.
Example 3 - CHALLENGE! Did you understand this? If no, don’t worry. This is a very advanced exercise. It is a fraction with a negative and fractional exponent. The first step in his example is to flip the fraction around an remove the minus. Then you square root the fraction before calculating it to the power of 4. If you have no problem with this type of expression, you can consider yourself a very accomplished mathematician in the area of fractions and indices.
ULTIMATE MATHS
WHERE MATHS IS AT YOUR FINGERTIPS!
ULTIMATE MATHS Becoming an Accomplished Mathematician Ultimate Maths is a professional maths website that gives students the opportunity to learn, revise and apply different maths skills. We provide a wide range of lessons and resources...