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This follows directly from the law for multiplication. For instance (using the symbol "^" for power):
10^3 x 10^2 = 10^5
Here, the exponents are added. Rearranging the multiplication, you get a division:
10^5 / 10^3 = 10^2
(Just like 6 / 2 = 3 follows from the fact that 2 x 3 = 6, for example.)
As you can see, it is obvious that the exponents must be subtracted in this case. If you want the more general case, take any multiplication with exponents (using the same base):
x^a times x^b = x^(a+b)
Rearranging to form a division:
x^(a+b) / x^a = x^b
What else can I help you with?
Why do you subtract the exponents when dividing powers with the same base?
When dividing powers with the same base, you subtract the exponents to reflect the principle of cancellation in multiplicative terms. This stems from the law of exponents which states that dividing two identical bases essentially removes one of the bases from the numerator and the denominator. By subtracting the exponents, you are effectively calculating how many times the base remains after the division. Thus, ( a^m / a^n = a^{m-n} ).
What is a6 divided by a5?
1.2
How do you divide a exponent?
If you have the same base on both of the exponents that you are dividing, all you have to do is subtract the exponent. For example if I have a problem like: 66/ 63, your answer will be 63.
When dividing two terms with the same base you what the exponents.?
When dividing two terms with the same base, you subtract the exponent of the denominator from the exponent of the numerator. This is expressed as ( a^m / a^n = a^{m-n} ). This rule applies as long as the base ( a ) is not zero.
How do you divide exponents of the same base?
By subtracting the two exponents from each other.NOTE: can only be done if the base is the same, like 23/21=22Also, make sure to subtract in the correct order, taking the top exponent and subtracting the one beneath it.
Why do you subtract the exponents when dividing powers with the same base?
When dividing powers with the same base, you subtract the exponents to reflect the principle of cancellation in multiplicative terms. This stems from the law of exponents which states that dividing two identical bases essentially removes one of the bases from the numerator and the denominator. By subtracting the exponents, you are effectively calculating how many times the base remains after the division. Thus, ( a^m / a^n = a^{m-n} ).
What is a6 divided by a5?
1.2
How do you divide a exponent?
If you have the same base on both of the exponents that you are dividing, all you have to do is subtract the exponent. For example if I have a problem like: 66/ 63, your answer will be 63.
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).
When dividing two terms with the same base what do you do to the exponents?
You would subtract the exponents. For instance, when solving (x-3)5/(x-3)2, you would find an answer of (x-3)3.
When dividing two terms with the same base you what the exponents.?
When dividing two terms with the same base, you subtract the exponent of the denominator from the exponent of the numerator. This is expressed as ( a^m / a^n = a^{m-n} ). This rule applies as long as the base ( a ) is not zero.
When multiplying terms with the same base you do what to the exponents?
Sum the exponents.
How do you divide exponents of the same base?
By subtracting the two exponents from each other.NOTE: can only be done if the base is the same, like 23/21=22Also, make sure to subtract in the correct order, taking the top exponent and subtracting the one beneath it.
Can divide powers with the same base by subtracting the exponents?
Yes, you can subtract the exponents, for example 5^3/5^2 = 5^3-2 = 5^1 Thats the same as 125/25 = 5
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).
When dividing two numbers with the same base?
i guess u subtract the exponents
What is a to the third power over a to the second power in simplest form?
As long as they have the same base (in this case a), to divide you just subtract the exponents. a3 ÷ a2 = a(3-2) = a
