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Dividing powers with the same base involves subtracting the exponents of the base. This means if you have a expression like ( a^m \div a^n ), it simplifies to ( a^{m-n} ). The base ( a ) must be the same in both terms for this rule to apply. This property is derived from the fundamental definition of exponents.
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What is the rule for multiplying powers with the same base and dividing power with the same base?
When multiplying powers with the same base, you add the exponents: (a^m \times a^n = a^{m+n}). Conversely, when dividing powers with the same base, you subtract the exponents: (a^m \div a^n = a^{m-n}). This rule applies as long as the base (a) is not zero.
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.
What is an example of the quotient of powers?
An example of the quotient of powers is when you divide two expressions with the same base. For instance, ( \frac{a^5}{a^2} ) simplifies to ( a^{5-2} = a^3 ). This demonstrates that when dividing powers with the same base, you subtract the exponents.
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} ).
Why do you subtract exponents when dividing powers of the same base?
When dividing powers of the same base, you subtract the exponents to reflect how many times the base is being divided. This is based on the principle that dividing a number by itself cancels it out, which corresponds to subtracting the exponent of the divisor from the exponent of the dividend. For example, (a^m \div a^n = a^{m-n}) effectively shows how many times the base remains after division. This rule simplifies calculations and maintains consistency in exponential expressions.
What is the rule for multiplying powers with the same base and dividing power with the same base?
When multiplying powers with the same base, you add the exponents: (a^m \times a^n = a^{m+n}). Conversely, when dividing powers with the same base, you subtract the exponents: (a^m \div a^n = a^{m-n}). This rule applies as long as the base (a) is not zero.
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.
What is an example of the quotient of powers?
An example of the quotient of powers is when you divide two expressions with the same base. For instance, ( \frac{a^5}{a^2} ) simplifies to ( a^{5-2} = a^3 ). This demonstrates that when dividing powers with the same base, you subtract the exponents.
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} ).
Why do you subtract exponents when dividing powers of the same base?
When dividing powers of the same base, you subtract the exponents to reflect how many times the base is being divided. This is based on the principle that dividing a number by itself cancels it out, which corresponds to subtracting the exponent of the divisor from the exponent of the dividend. For example, (a^m \div a^n = a^{m-n}) effectively shows how many times the base remains after division. This rule simplifies calculations and maintains consistency in exponential expressions.
How do you simplify exponents or powers in algebra?
When multiplying exponents with the same base add them: x^3*x^2 = x^5 When dividing exponents with the same base subtract them: x^3/x^2 = x^1 or x
What do you do when your dividing powers?
When dividing powers with the same base, you subtract the exponents. For example, ( a^m \div a^n = a^{m-n} ). This rule simplifies calculations and helps maintain consistency in exponent rules. If the bases are different, you cannot directly apply this rule and must evaluate each term separately.
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.
What do power quotient means in math?
In mathematics, a power quotient typically refers to the result of dividing two exponential expressions with the same base. According to the laws of exponents, when dividing powers with the same base, you subtract the exponents: ( a^m / a^n = a^{m-n} ). This concept is essential in simplifying expressions involving exponents and plays a crucial role in algebra and higher-level mathematics.
When do add exponents?
when you multiply powers with the same base.
Dividing the powers of the government as the colonial charters did is called?
Separation of powers is what dividing the powers of government is called.
When dividing two numbers with the same base?
i guess u subtract the exponents
