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To simplify, you write one copy of the base, then add the exponent. Example:x^5 times x^3 = x^8
In the case of positive integer exponents, this can easily be derived by writing each power as a repeated multiplication. However, this law is also valid for negative or fractional exponents.
What else can I help you with?
What happens when you multiply two variables with different exponents?
When you multiply two variables with different exponents, the exponents are added. For example, if you multiply x^2 by x^3, the result is x^(2+3) = x^5. Similarly, if you multiply x^3 by x^(-2), the result is x^(3+(-2)) = x^1 = x.
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 multiply two different number with two different exponents?
the answer is simple you can not
What do you do when you multiply two bases that are the same?
When you multiply two bases that are the same, you add their exponents. For example, if you have (a^m \times a^n), the result is (a^{m+n}). This rule applies only when the bases are identical; if the bases differ, you cannot combine them in this way.
What does the product rule of exponents say?
When a base is raised to a power inside a quantity , multiply the two exponents to solve.
What happens when you multiply two variables with different exponents?
When you multiply two variables with different exponents, the exponents are added. For example, if you multiply x^2 by x^3, the result is x^(2+3) = x^5. Similarly, if you multiply x^3 by x^(-2), the result is x^(3+(-2)) = x^1 = x.
When you have two different exponents do you add them or multiply them?
Multiply
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 multiply two different number with two different exponents?
the answer is simple you can not
What does the product rule of exponents?
When a base is raised to a power inside a quantity , multiply the two exponents to solve.
If two exponents have the same factor or base what happens to the exponents when the exponents are multipled?
The exponents are added.
What do you do when you multiply two bases that are the same?
When you multiply two bases that are the same, you add their exponents. For example, if you have (a^m \times a^n), the result is (a^{m+n}). This rule applies only when the bases are identical; if the bases differ, you cannot combine them in this way.
What does the product rule of exponents say?
When a base is raised to a power inside a quantity , multiply the two exponents to solve.
What is the relationship between the exponents of the base and the exponent of the product?
when two numbers are multiplied together that are exponents you multiply the bases amd add the exponents the relationship would simply be that the product exponents are the sum of the exponents being multiplied in the question
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.
How do you multiply exponets and fractions?
When you multiply fractions together, you multiply the numerators together to get the numerator of the answer and you multiply the denominators together to get the denominator of the answer. For example: 1/2 * 2/3 = (1*2)/(2*3) = 2/6 = 1/3. When multiplying exponents of the same base together, you simply add the two exponents and make that the exponent of the same base. For example: 22 * 23 = 25 = 32. Or for the algebra-savvy: x2 * x3 = x5.
What is the sum of the exponents for two variables called?
The sum of the exponents for two variables in a polynomial or algebraic expression is called the degree of the term. For example, in the term (x^m y^n), the degree is (m + n). This concept helps determine the overall degree of the polynomial when combining multiple terms.
