%5E3-as-a-single-exponent.jpeg "(7^2)^3 As A Single Exponent")
Simplifying Exponents: (7^2)^3
In mathematics, we often encounter expressions with exponents raised to other exponents. This can seem complicated at first, but there's a simple rule that allows us to simplify these expressions.
The Rule of Exponents
The rule states that when raising a power to another power, we multiply the exponents together. In other words:
(a^m)^n = a^(m*n)
Applying the Rule to (7^2)^3
Let's apply this rule to our example: (7^2)^3
- Identify the exponents: We have 2 as the exponent of 7, and 3 as the exponent of the entire expression (7^2).
- Multiply the exponents: 2 * 3 = 6
- Rewrite the expression: (7^2)^3 = 7^(2*3) = 7^6
Conclusion
Therefore, (7^2)^3 can be expressed as a single exponent, 7^6. This simplification makes it easier to understand and calculate the value of the expression.