nothing, keep the exponents the same, remember you can only add or subtract when the exponents are the same
You keep them the same if they have different bases
Exponents represent repeated multiplication of a base number, and the rules of exponents state that when multiplying two powers with the same base, you add the exponents (e.g., (a^m \times a^n = a^{m+n})). However, when you have a product with exponents, you cannot simply add the exponents because they represent different operations. Each exponent is tied to its specific base, so adding them would misrepresent the actual multiplication of the numbers involved. For example, (a^m \times b^n) cannot be simplified by adding the exponents since (a) and (b) are different bases.
To simplify an equation using exponents, first identify the base numbers and their respective powers. Apply the laws of exponents, such as the product of powers (adding exponents when multiplying like bases), the quotient of powers (subtracting exponents when dividing like bases), and the power of a power (multiplying exponents when raising a power to another power). Combine like terms and reduce any fractions as needed. Finally, express the equation in its simplest form.
When adding numbers with exponents, you can only combine the terms if they have the same base and the same exponent. For example, (2^3 + 2^3) can be simplified to (2 \times 2^3 = 2^4), which equals (16). However, if the bases or exponents differ, you cannot combine them directly; you must leave them as separate terms.
Combining laws of exponents refers to the rules that govern the manipulation of expressions involving powers. Key laws include the product of powers (adding exponents when multiplying like bases), the quotient of powers (subtracting exponents when dividing like bases), and the power of a power (multiplying exponents when raising a power to another power). These rules help simplify expressions and solve equations involving exponents efficiently. Understanding these laws is essential for working with algebraic expressions in mathematics.
You keep them the same if they have different bases
You have to add the exponents. It's best if you just remember it. You can also consider what happens when you multiply something like:(2 x 2 x 2) x (2 x 2) As you can notice, the number of factors get added. That's like adding the exponents.
Exponents represent repeated multiplication of a base number, and the rules of exponents state that when multiplying two powers with the same base, you add the exponents (e.g., (a^m \times a^n = a^{m+n})). However, when you have a product with exponents, you cannot simply add the exponents because they represent different operations. Each exponent is tied to its specific base, so adding them would misrepresent the actual multiplication of the numbers involved. For example, (a^m \times b^n) cannot be simplified by adding the exponents since (a) and (b) are different bases.
To simplify an equation using exponents, first identify the base numbers and their respective powers. Apply the laws of exponents, such as the product of powers (adding exponents when multiplying like bases), the quotient of powers (subtracting exponents when dividing like bases), and the power of a power (multiplying exponents when raising a power to another power). Combine like terms and reduce any fractions as needed. Finally, express the equation in its simplest form.
Exponents are numbers that simplify the amount of times a number multiplies by itself. For example, 5^3 would be equal to 5x5x5 which equals 125. In that same number, 5 would be the base and 3 would be the exponent, (aka) the little number on the top right of another number. And yes, exponents CAN have exponents.
When adding numbers with exponents, you can only combine the terms if they have the same base and the same exponent. For example, (2^3 + 2^3) can be simplified to (2 \times 2^3 = 2^4), which equals (16). However, if the bases or exponents differ, you cannot combine them directly; you must leave them as separate terms.
Adding powers involves combining expressions that have the same base and exponent. If the bases and exponents are identical, you can simply add the coefficients in front of the powers. For example, (3x^2 + 5x^2 = (3 + 5)x^2 = 8x^2). However, if the bases or exponents differ, you cannot directly combine them without additional operations.
Combining laws of exponents refers to the rules that govern the manipulation of expressions involving powers. Key laws include the product of powers (adding exponents when multiplying like bases), the quotient of powers (subtracting exponents when dividing like bases), and the power of a power (multiplying exponents when raising a power to another power). These rules help simplify expressions and solve equations involving exponents efficiently. Understanding these laws is essential for working with algebraic expressions in mathematics.
When multiplying something with exponents, you add it. When dividing something with exponents, you subtract it.
Add the exponents
When multiplying common bases, you add the exponents. For example, if you have ( a^m \times a^n ), the result is ( a^{m+n} ). This property applies to any real number base, provided the base is not zero.
you do not do anything when you add numbers with exponents. you just figure out the answer. it is only if you multiply numbers with exponents, where you add the exponents..