Add the indices
You add them.
Sum the exponents.
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.
When multiplying two terms with the same base, you add the exponents. For example, if you have ( a^m \times a^n ), the result is ( a^{m+n} ). This rule applies to any non-zero base.
If you are multiplying numbers with exponents, and the base is the same, you can just add exponents. For example, 104 x 105 = 109.
If you are multiplying powers of the same base (like 24 times 211), yes, you add the exponents.
Same as multiplying any number by itself once or many times.
When multiplying powers with the same base, you add the exponents due to the properties of exponents that define multiplication. This is based on the idea that multiplying the same base repeatedly involves combining the total number of times the base is used. For example, (a^m \times a^n = a^{m+n}) because you are effectively multiplying (a) by itself (m) times and then (n) times, resulting in a total of (m+n) multiplications of (a). This rule simplifies calculations and maintains consistency in mathematical operations involving exponents.
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).
If the base numbers or variables are the same, you add the exponents.
Multiplying is the same as repeated addition.
To multiply powers with the same base, you simply add their exponents. For example, if you have ( a^m \times a^n ), the result is ( a^{m+n} ). This rule applies as long as the bases are identical.