(7%5E3).jpeg "(7^-8)(7^3)")
Simplifying Exponents: (7^-8)(7^3)
This problem involves simplifying an expression with exponents. Here's how to solve it:
Understanding the Rules
- Product of Powers: When multiplying exponents with the same base, you add the powers. Mathematically, this is: x^m * x^n = x^(m+n)
Applying the Rule
- Identify the base: In this case, the base is 7.
- Add the exponents: We have -8 + 3 = -5
- Combine the base and the new exponent: This gives us 7^-5
Dealing with Negative Exponents
- Negative exponents indicate reciprocals: 7^-5 is the same as 1/7^5.
Final Solution
Therefore, (7^-8)(7^3) simplifies to 1/7^5 or 1/16,807.