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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.
Definition multiply and divide powers that have the same base?
Ok, basically here:5^65 is the base, 6 is the power.So if you have:5^8 * 5^9it would equal 5^175^8 / 5^9would equal 5^-2 or 5^1/2
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.
Why do you subtract exponents when you dividing powers?
When dividing powers with the same base, you subtract the exponents to simplify the expression based on the properties of exponents. This is derived from the definition of exponents, where dividing (a^m) by (a^n) (both with the same base (a)) can be thought of as removing (n) factors of (a) from (m) factors of (a), resulting in (a^{m-n}). This rule helps maintain consistency and simplifies calculations involving powers.
Why do we add the exponents when we multiply terms with the same base?
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.
When do add exponents?
when you multiply powers with the same base.
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).
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.
Definition multiply and divide powers that have the same base?
Ok, basically here:5^65 is the base, 6 is the power.So if you have:5^8 * 5^9it would equal 5^175^8 / 5^9would equal 5^-2 or 5^1/2
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.
Why do we add the exponents when we multiply terms with the same base?
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.
To multiply powers with the same exponents what do you do?
yes they are the same 4^3 = 4*4*4=64
If the base are different and powers are same in a equation then can the power be canceled?
no
What is quotient of powers?
When you divide powers having the same base, subtract the numerator from the denomenator. Put the base in the part of the fraction where the original exponent was larger.
What is the rule for multiply numbers with the same base but different exponents?
base x base result x Exponent
What is the definition of similar terms in algebra?
Numbers that have the same variable or powers of a variable, such as 2x and 6x.
How do you multiphly powers with the same base?
Add them. 102 x 103 = 105
