$\sqrt[3]{3375}^{18-4}$
Answer (2)
Simplify the exponent: 18 − 4 = 14 .
Find the cube root of 3375: 3 3375 = 15 .
Raise 15 to the power of 14: 1 5 14 = 29192926025390625 .
The final answer is 29192926025390625 .
Explanation
Understanding the problem We are given the expression 3 3375 18 − 4 and we need to simplify it.
Simplifying the exponent First, let's simplify the exponent: 18 − 4 = 14 . So, the expression becomes 3 3375 14 .
Calculating the cube root Next, we need to find the cube root of 3375. We can recognize that 1 5 3 = 15 × 15 × 15 = 225 × 15 = 3375 . Therefore, 3 3375 = 15 .
Raising to the power Now, we have 1 5 14 . We need to calculate this value. 1 5 14 = 29192926025390625 .
Examples
Exponents and roots are fundamental in calculating growth rates, such as population increase or compound interest. For example, if a population grows at a certain percentage annually, you can use exponents to project future population sizes. Similarly, roots can help determine the initial investment needed to reach a specific financial goal, given a fixed interest rate and time period. Understanding these concepts allows for informed decision-making in various real-world scenarios.
To simplify 3 3375 18 − 4 , we calculate each part step by step: first, we simplify the exponent to 14, find that the cube root of 3375 is 15, and lastly, compute 1 5 14 to get the final answer, 29192926025390625 .
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