Express a number in index form. In previous videos, we have learned how to find the value of an index number. In this video, we are going to discuss how to find the index form for a given number. Let's start with these five numbers. Okay, the first one is 1 million. This one is easy because we can straightaway tell that this is equal to 10 times 10 times 10 times 10 times 10 times 10, or 10 to the power of 6. The next number is 81. We know that 81 is equal to 9 times 9, and we also know that 9 is equal to 3 times 3. So, 81 is equal to 3 to the power of 4. Next, we have 0.0081. We have 4 decimal places here, so we can deduce that this is equal to 0.3 times 0.3 times 0.3 times 0.3, or 0.3 to the power of 4. Moving on to the negative number -32. You should be able to tell that 32 is equal to 2 times 2 times 2 times 2 times 2. However, since this is a negative number, we need to include negative signs for each 2. Thus, we have (-2) to the power of 5. Next is 1/25. You should be able to tell that 1/25 is equal to 1/5 times 1/5 times 1/5, or (1/5) to the power of 3. Lastly, we have 16/81. We can tell that 16 is equal to 4 times 4, and 81 is equal to 3 times 3 times 3 times 3. Therefore, 16/81 can be written as 4/9 squared, or 2/3 to the power of 4. Now, let's move on to other examples. Let's start with 1/X to the power of 4. If you remember, we learned that a to the power of -n is equal...