%5E3-as-a-single-power.jpeg "(10^2)^3 As A Single Power")
Simplifying Exponents: (10^2)^3 as a single power
When working with exponents, we often encounter expressions like (10^2)^3. This might seem daunting at first, but there's a simple rule to simplify it into a single power.
The Rule of Exponent Powers
The rule states: (a^m)^n = a^(m*n)
This means that when raising a power to another power, you multiply the exponents.
Applying the Rule
Let's apply this rule to our expression (10^2)^3:
- Identify the base and exponents: The base is 10, the first exponent is 2, and the second exponent is 3.
- Multiply the exponents: 2 * 3 = 6
- Rewrite the expression: (10^2)^3 = 10^6
Therefore, (10^2)^3 can be simplified as a single power of 10^6.
Understanding the Concept
Essentially, (10^2)^3 means you're multiplying 10^2 by itself three times:
(10^2)^3 = 10^2 * 10^2 * 10^2
Since multiplying powers with the same base means adding the exponents, we get:
10^2 * 10^2 * 10^2 = 10^(2+2+2) = 10^6
This further reinforces the rule and explains why (10^2)^3 simplifies to 10^6.