Compute each term separately when either the bases, the exponents or both are different. Check to see if the terms you want to multiply have the same base. You can only multiply terms with exponents when the bases are the same. Multiply the terms by adding the exponents. Compute each term separately if the bases in the terms are not the same.
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How to Factorise a Quadratic Expression. How to Find Terms in an Algebra Expression. Solution: Here, the bases and the powers are different.
Therefore, each term will be solved separately. Let us recall the rules for multiplying exponents with the same base and with different bases in the following figure. Negative Exponents tell us how many times we need to multiply the reciprocal of the base. In other words, we can convert a negative exponent to a positive one by writing the reciprocal of the given expression and then we can solve it like a positive expression.
For multiplying negative exponents, we need to follow certain rules that are given in the following table.
Solution: Here, the base is same, that is, 2. The powers are negative and different. Solution: Here, the bases are different and the negative powers are the same. Solution: Here, both the bases and the negative powers are different. If the base of an expression is a variable, we use the same exponent rules of multiplication that are used for numbers.
Solution: The variable base is the same, that is, 'a'. When the variable bases are different and the powers are the same, the bases are multiplied first. When the variable bases and the powers are different, the terms are evaluated separately and then multiplied.
In this section, we will explore the multiplication of exponents where the bases have a square root. It should be noted that the exponent rules remain the same if the bases are square roots. Apart from this, one important point to be remembered is that we can convert radicals to rational exponents and then multiply the given expressions. Now, let us use the exponent rules of multiplication that are applicable to expressions in which the bases are square roots.
Solution: The square root bases are the same. When the square root bases are different and the powers are the same, the bases are multiplied first. Solution: The square root bases are different and the powers are the same. When the square root bases and the powers are different, the exponents are evaluated separately and then multiplied. Solution: The square root bases and the powers are different. If the base of an expression is a fraction which is raised to an exponent, we use the same exponent rules that are used for bases that are whole numbers.
Observe the following table to see the different scenarios. Solution: Here, the fractional bases are different but the powers are the same. Solution: Here, the fractional bases are the same. Solution: Here, the fractional bases and the powers are different. So, first, we will solve each term separately and then move further. When a term has a fractional power, it is called a fractional exponent. Let us understand the rules that are applied to multiply fractional exponents with the help of the following table.
Solution: Here, the bases are the same. Solution: Here, the bases are different but the fractional powers are the same. Exponents: Basic Rules - PurpleMath. Exponent Rules - RapidTables. Laws of Exponents - MathisFun.
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