%5E2-as-a-single-exponent.jpeg "(10^7)^2 As A Single Exponent")
Simplifying Exponential Expressions: (10^7)^2
In mathematics, we often encounter expressions involving exponents. One common operation is raising a power to another power. Let's explore how to simplify the expression (10^7)^2 into a single exponent.
The Rule of Exponents
The key principle we'll use is the rule of exponents for powers of powers:
(a^m)^n = a^(m*n)
This rule states that when raising a power (a^m) to another power (n), we multiply the exponents.
Applying the Rule
Let's apply this rule to our expression:
(10^7)^2 = 10^(7*2)
Simplifying the multiplication, we get:
10^(7*2) = 10^14
Therefore, (10^7)^2 can be expressed as a single exponent: 10^14.
Conclusion
By applying the rule of exponents for powers of powers, we were able to simplify (10^7)^2 into 10^14. Understanding and applying these rules are essential for effectively working with exponential expressions in mathematics.