Write the expression as an exponent with a base 2 and find its value: [tex]$16 \cdot 32$[/tex]
Answer (2)
Express 16 as a power of 2: 16 = 2 4 .
Express 32 as a power of 2: 32 = 2 5 .
Rewrite the expression: 16 c d o t 32 = 2 4 c d o t 2 5 .
Apply the exponent rule and calculate: 2 4 c d o t 2 5 = 2 4 + 5 = 2 9 = 512 . The final answer is 512 .
Explanation
Understanding the Problem We are asked to express the product 16 c d o t 32 as an exponent with base 2 and then find its value.
Expressing 16 as a power of 2 First, we express 16 as a power of 2. Since 2 4 = 2 c d o t 2 c d o t 2 c d o t 2 = 16 , we have 16 = 2 4 .
Expressing 32 as a power of 2 Next, we express 32 as a power of 2. Since 32 = 2 c d o t 2 c d o t 2 c d o t 2 c d o t 2 = 2 5 , we have 32 = 2 5 .
Rewriting the expression Now we can rewrite the original expression as 16 c d o t 32 = 2 4 c d o t 2 5 .
Applying the exponent rule Using the exponent rule a m c d o t a n = a m + n , we have 2 4 c d o t 2 5 = 2 4 + 5 = 2 9 .
Calculating the value of 2^9 Finally, we calculate the value of 2 9 . We have 2 9 = 512 .
Final Answer Therefore, 16 c d o t 32 = 2 9 = 512 .
Examples
Exponents are useful in computer science when dealing with memory sizes. For example, a kilobyte (KB) is 2 10 bytes, a megabyte (MB) is 2 20 bytes, and a gigabyte (GB) is 2 30 bytes. Understanding exponents helps in grasping the scale and relationships between these units.
The expression 16 ⋅ 32 can be expressed as 2 9 since 16 = 2 4 and 32 = 2 5 . This results in a value of 512. Therefore, the final answer is 512 .
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