%5E6-as-a-single-exponent.jpeg "(4^5)^6 As A Single Exponent")
Understanding Exponents: Evaluating (4^5)^6 as a Single Exponent
Exponents are a fundamental concept in mathematics, and understanding how to work with them is essential for success in various mathematical disciplines. In this article, we will explore how to evaluate the expression (4^5)^6 as a single exponent.
What are Exponents?
Before we dive into the evaluation of the expression, let's quickly review what exponents are. An exponent is a small number that is raised to a power, indicating that a base number should be multiplied by itself as many times as the exponent indicates. For example, in the expression 2^3, the base is 2, and the exponent is 3, meaning 2 is multiplied by itself three times: 2 × 2 × 2 = 8.
Evaluating (4^5)^6
Now, let's evaluate the expression (4^5)^6. To do this, we need to follow the order of operations (PEMDAS):
- Evaluate the expression inside the parentheses: 4^5 = 1024
- Raise the result to the power of 6: 1024^6
To raise 1024 to the power of 6, we can use the rule of exponents that states:
a^(mn) = (a^m)^n
In this case, a = 1024, m = 5, and n = 6. Using the rule, we get:
1024^6 = ((1024^5))^6 = (4^5)^6 = 4^(5×6) = 4^30
Simplifying the Expression
So, (4^5)^6 is equal to 4^30. This is our final answer, which is a single exponent.
Conclusion
In conclusion, evaluating (4^5)^6 as a single exponent involves following the order of operations and using the rule of exponents. By applying these rules, we can simplify the expression to 4^30. Understanding exponents is crucial in mathematics, and this skill will help you tackle more complex expressions and equations with confidence.
