%5E7-as-a-single-exponent.jpeg "(4^5)^7 As A Single Exponent")
Raising a Power to a Power: (4^5)^7 as a Single Exponent
When working with exponents, we often encounter expressions that involve raising a power to a power. One such example is (4^5)^7. In this article, we will explore how to simplify this expression and express it as a single exponent.
The Rule of Exponentiation
To simplify expressions involving exponents, we need to remember the rule of exponentiation:
a^(mn) = (a^m)^n
This rule states that when we raise a power to another power, we can simplify the expression by raising the base to the product of the exponents.
Applying the Rule to (4^5)^7
Using the rule of exponentiation, we can simplify (4^5)^7 as follows:
(4^5)^7 = 4^(5*7) = 4^35
Thus, we can express (4^5)^7 as a single exponent: 4^35.
Conclusion
In conclusion, simplifying expressions involving exponents requires us to remember the rule of exponentiation. By applying this rule, we can simplify complex expressions like (4^5)^7 and express them as a single exponent. In this case, we found that (4^5)^7 is equivalent to 4^35.
Remember
When working with exponents, always remember to apply the rule of exponentiation:
a^(mn) = (a^m)^n
This rule will help you simplify complex expressions and express them as single exponents.
