%5E3.jpeg "(m^2n^7)^3")
Simplifying Exponential Expressions: (m^2n^7)^3
In mathematics, we often encounter expressions with exponents. Simplifying these expressions involves understanding the rules of exponents. One such rule states that when raising a power to another power, you multiply the exponents. Let's apply this rule to the expression (m^2n^7)^3.
Breaking Down the Expression
- (m^2n^7)^3 means we are multiplying (m^2n^7) by itself three times.
- (m^2n^7) * (m^2n^7) * (m^2n^7)
Applying the Rule
Using the rule mentioned earlier, we can simplify this by multiplying the exponents of each variable by the outer exponent (3 in this case):
- m^(23) * n^(73)
Final Result
Simplifying further, we get:
- m^6 * n^21
Therefore, (m^2n^7)^3 is equivalent to m^6n^21.
This process demonstrates how to simplify expressions involving exponents by applying the appropriate rules. Remember, understanding these rules is crucial for effectively working with exponents in various mathematical contexts.