Write the expression as an exponent:
[tex]$6^{15} \cdot 36$[/tex]
Answer (2)
Rewrite 36 as a power of 6: 36 = 6 2 .
Substitute the expression for 36 in the original expression: 6 15 ".36 = 6 15 ". 6 2 .
Use the property a m ". a n = a m + n to write the expression as a single exponent: 6 15 ". 6 2 = 6 15 + 2 = 6 17 .
The expression 6 15 ".36 can be written as 6 17 .
Explanation
Understanding the problem We are asked to write the expression 6 15 ".36 as an exponent. This means we want to express the given expression in the form 6 k for some integer k .
Rewriting 36 as a power of 6 First, we need to rewrite 36 as a power of 6. Since 36 = 6".6 = 6 2 , we can rewrite the expression as 6 15 ". 6 2 .
Using the exponent property Now, we use the property of exponents that states a m ". a n = a m + n . In our case, a = 6 , m = 15 , and n = 2 . Therefore, 6 15 ". 6 2 = 6 15 + 2 = 6 17 .
Final answer Thus, the expression 6 15 ".36 can be written as 6 17 .
Examples
Exponents are useful in many real-world situations, such as calculating compound interest or modeling population growth. For example, if a population grows by 5% each year, we can use exponents to calculate the population after a certain number of years. Similarly, exponents are used in computer science to represent binary numbers and in physics to describe exponential decay.
The expression 6 15 ⋅ 36 can be rewritten as 6 17 by substituting 36 with 6 2 and using the property of exponents to combine them. Thus, 6 15 ⋅ 36 = 6 15 + 2 = 6 17 .
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