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When we multiply terms with the same base, we add the exponents due to the definition of exponentiation. Each exponent indicates how many times the base is multiplied by itself, so when we multiply two terms with the same base, we are essentially combining all those multiplications. For example, (a^m \times a^n) can be rewritten as (a) multiplied by itself (m) times and then (n) additional times, resulting in (a^{m+n}). This property helps simplify calculations and maintain consistency within the rules of exponents.
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Why do we add exponents when we multiply terms with the same base?
When multiplying terms with the same base, we add the exponents because of the fundamental property of exponents that states (a^m \times a^n = a^{m+n}). This property arises from the repeated multiplication of the base: for example, (a^m) represents multiplying the base (a) by itself (m) times, and (a^n) represents multiplying it (n) times. Therefore, when these two terms are multiplied, the total number of times the base (a) is multiplied is (m + n).
What is the rule for multiply numbers with the same base but different exponents?
base x base result x Exponent
What property can you use to multiply the expressions with exponents?
The Addition Property of Exponents. To multiply powers with the same base, add the exponents. e.g. 34 x 37 = 311, x2x3 = x5, and (3x2yz3)(2x5y2z) = 6x7y3z4.
What does it mean to multiply two powers having the same base and add the exponents?
This is one of the laws of exponents, which states that xa * xb = x(a+b) The base is x, and the two powers (or exponents) are a and b.
How do you solve multiplication with like terms?
Just multiply the coefficients, leave the variable the same, and add the exponents.
When multiplying terms with the same base you do what to the exponents?
Sum the exponents.
When do add exponents?
when you multiply powers with the same base.
When multiplying a number exponents that are squared do you add or multiply?
If the base numbers or variables are the same, you add the exponents.
What is the rule for multiply numbers with the same base but different exponents?
base x base result x Exponent
What property can you use to multiply the expressions with exponents?
The Addition Property of Exponents. To multiply powers with the same base, add the exponents. e.g. 34 x 37 = 311, x2x3 = x5, and (3x2yz3)(2x5y2z) = 6x7y3z4.
What does it mean to multiply two powers having the same base and add the exponents?
This is one of the laws of exponents, which states that xa * xb = x(a+b) The base is x, and the two powers (or exponents) are a and b.
How do you solve multiplication with like terms?
Just multiply the coefficients, leave the variable the same, and add the exponents.
Why don't we change the exponents during like terms?
Exponents are higher in priority in terms of the order of operations, and do not combine in the same way as you would simple add/subtract/multiply/divide. So, if you have: 26 + 24 This is a polynomial in base 2 with different powers. It would be this in binary: 1010000 ...which would not be the same as 210: 1000000000 In order to be able to change exponents, you have to be multiplying factors using the same base, as in: 26 * 24 = 210 ...because the exponents are also indicating how many times you are multiplying each base by itself, and multiplication is the same as the basal function of the exponent (repeated multiplication).
What is a rule that works for multiplying powers of the same base in exponents?
To multiply powers with the same base, you add the exponents. For example, 10^2 x 10^3 = 10^5. Similarly, to divide powers with the same base, you subtract the exponents. For example, 10^3 / 10^5 = 10^(-2).
How do you multiply exponents with different coefficients?
To multiply exponents with different coefficients, you first multiply the coefficients together and then apply the exponent rule. For example, if you have (a^m) and (b^n), the result of multiplying them is (ab^{mn}). The exponents remain the same unless they have the same base, in which case you add the exponents together. So, (a^m \cdot a^n = a^{m+n}).
Multiply and simplify 5 to the 9th power X 5 to the 7th power?
Since the base is the same, just add the exponents. 59 x 57 = 516.Since the base is the same, just add the exponents. 59 x 57 = 516.Since the base is the same, just add the exponents. 59 x 57 = 516.Since the base is the same, just add the exponents. 59 x 57 = 516.
What is terms with the same variables raised to the same exponents?
like terms
