To provide the best experiences, we use technologies like cookies to store and/or access device information. Consenting to these technologies will allow us to process data such as browsing behavior or unique IDs on this site. Not consenting or withdrawing consent, may adversely affect certain features and functions.
The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network.
The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user.
The technical storage or access that is used exclusively for statistical purposes.
The technical storage or access that is used exclusively for anonymous statistical purposes. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you.
The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes.
3 Responses
Totally easy to mix up-I do it too: when multiplying the same base, add exponents; when raising a power to a power, multiply exponents. So 2^3 × 2^2 = 2^(3+2) = 2^5 = 32, while (2^3)^2 = 2^(3·2) = 2^6 = 64.
When the bases match and you multiply, the exponents add: 2^3 × 2^2 = 2^(3+2) = 2^5 = 32.
But a power of a power makes them multiply: (2^3)^2 = 2^(3·2) = 2^6 = 64.
Easy to mix up-same symbols, different jobs. Here’s the rule of thumb: when you’re multiplying matching bases (like 2^3 × 2^2), you add the exponents: a^m × a^n = a^(m+n). When you’ve got a power raised to another power (like (2^3)^2), you multiply the exponents: (a^m)^n = a^(m·n). Side-by-side means add, stacked means multiply.
Quick check with your numbers:
– 2^3 × 2^2 = (2·2·2) × (2·2) = five 2’s multiplied = 2^5 = 32.
– (2^3)^2 = (2·2·2)^2 = (2·2·2)(2·2·2) = six 2’s multiplied = 2^6 = 64.
If you like a mental trick: imagine how many 2’s you’re actually stringing together. Side-by-side groups just join up (add), stacking a power on a power doubles/triples/etc. the count (multiply).