%5E2-simplified.jpeg "(2^3)^2 Simplified")
Simplifying (2^3)^2
When we see an expression like (2^3)^2, our first instinct might be to calculate the value inside the parentheses first. But do we really need to do that? Let's explore how to simplify this expression.
Understanding Exponential Rules
Before we dive into the simplification, it's essential to understand the rules of exponents. One of the most important rules is the power of a power rule, which states:
a^(m)^n = a^(mn)
This rule allows us to simplify expressions where there are multiple layers of exponents.
Simplifying (2^3)^2
Now, let's apply the power of a power rule to our expression (2^3)^2. We can rewrite it as:
(2^3)^2 = 2^(3*2)
Using the rule, we can multiply the exponents: 3*2 = 6. So, our simplified expression becomes:
2^6
Calculating the Value
If we want to calculate the actual value of the expression, we can raise 2 to the power of 6:
2^6 = 64
And that's our final answer!
Conclusion
In conclusion, we learned how to simplify the expression (2^3)^2 using the power of a power rule. By applying this rule, we can simplify the expression to 2^6, and if needed, calculate its value, which is 64.
