Rewrite the product as an exponent:
[tex]$2^6 \cdot 2^4$[/tex]
Answer (2)
Recognize that when multiplying exponents with the same base, you add the exponents.
Apply the rule a m c d o t a n = a m + n to the expression 2 6 c d o t 2 4 , which gives 2 6 + 4 .
Calculate the sum of the exponents: 6 + 4 = 10 .
Rewrite the product as an exponent: 2 10 .
Explanation
Understanding the problem We are asked to rewrite the product 2 6 c d o t 2 4 as a single exponent. To do this, we need to remember the rules of exponents.
Using the exponent rule The key rule we'll use is that when multiplying exponents with the same base, we add the exponents. That is, a m c d o t a n = a m + n .
Applying the rule to the problem In our case, the base is 2, and the exponents are 6 and 4. So, we have 2 6 c d o t 2 4 = 2 6 + 4 .
Calculating the exponent Now, we simply add the exponents: 6 + 4 = 10 . Therefore, 2 6 c d o t 2 4 = 2 10 .
Final Answer So, the product 2 6 c d o t 2 4 can be rewritten as 2 10 .
Examples
Exponents are used to calculate compound interest. For example, if you invest money in a bank account that pays compound interest, the amount of money you have at the end of each year can be calculated using an exponent. Also, exponents are used in computer science to calculate memory sizes (e.g., kilobytes, megabytes, gigabytes) and processing power.
To rewrite 2 6 ⋅ 2 4 as a single exponent, you add the exponents together, following the rule a m ⋅ a n = a m + n . This results in 2 10 , so the expression rewrites to 2 10 .
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