In words, we can say 10 4 could be called "10 to the fourth power", "10 to the power 4" or "10 to the 4"ġ0 to the power of 6 = 10 × 10 × 10 × 10 × 10 × 10 = 1000000Ī negative power means how many times we have to divide by the number. In words, we can say 10 3 could be called "10 to the third power", "10 to the power 3" or simply "10 cubed".ġ0 to the power of 4 equals 10 × 10 × 10 × 10 = 10000. Instead of having lots of zeros, we can show how many powers of 10 will make that many zeros.ĥ thousand is 5 times a thousand. "Powers of 10" is a very useful tool when we have to express large or small numbers. Rule 8: If an index is in the form of a fraction it can be represented in the radical form.Ģ to the power of 10 = 2 10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024. We have to divide the bases and raise the same index to it. Rule 7: When two variables with different bases are given, and the same indices are divided. Rule 6: When two variables with different bases, but the same indices are multiplied together, we have to multiply its base and raise the same index to multiplied variables. Rule 5: When a variable with some index is again raised with a different index, then both the indices are multiplied together raised to the power of the same base. Rule 4: To divide two variables with the same base, we need to subtract the power of the denominator from the power of the numerator and raise it to that base. Rule 3: If we multiply two variables with the same base, we need to add their powers and raise them to that base. Rule 2: If the index value is negative, then it can be shown as the reciprocal of the positive index raised to the same variable. Rule 1: If a constant or variable has index as ‘0’, then the value of the result will be one. Following are the rules we need to follow: We follow these rules while performing algebraic operations on indices. There are some fundamental rules or laws of indices that are necessary to understand before we start solving problems with indices. It is an easy way of writing big numbers and calculations. The index says that a particular number (or base) is to be multiplied by itself or the number of times equal to the index raised to it. Here, a is called base and m is the index. It shows the number of times the given number has to be multiplied.
![power of ten in standard notation power of ten in standard notation](https://image.slideserve.com/937256/powers-of-ten-and-scientific-notation-l.jpg)
The index value is also known as powers or exponents. Index of a variable is a value that is raised to the power of the variable.
![power of ten in standard notation power of ten in standard notation](https://image.slidesharecdn.com/fishlocklessononestandardform-091111080523-phpapp01/95/fishlock-lesson-one-standard-form-2-728.jpg)
In algebra, mostly we deal with indices in terms of numbers. The constant value is fixed that cannot be changed, whereas a variable can be assigned any number or we can say its value can be changed. In algebra, we come across constants and variables. For example, in number 2 5, 5 is the index of 2. In Mathematics, Index (indices) is the power or exponent which is raised to a number or a variable.