Simplifying Exponents: 3^2 x 3^5
In this article, we will simplify the expression 3^2 x 3^5 using the rules of exponents.
The Rules of Exponents
Before we dive into simplifying the expression, let's review the rules of exponents:
- Product of Powers: When we multiply two expressions with the same base, we add the exponents. This can be written as:
a^m x a^n = a^(m+n)
- Power of a Power: When we raise an expression with an exponent to another power, we multiply the exponents. This can be written as:
(a^m)^n = a^(mn)
Simplifying 3^2 x 3^5
Now, let's apply the rules of exponents to simplify the expression 3^2 x 3^5:
3^2 x 3^5 = ?
Using the Product of Powers rule, we can rewrite the expression as:
3^(2+5)
= 3^7
Therefore, the simplified expression is 3^7.
Conclusion
In this article, we have successfully simplified the expression 3^2 x 3^5 using the rules of exponents. By applying the Product of Powers rule, we were able to simplify the expression to 3^7. Remember to always follow the rules of exponents when working with expressions involving powers.
