%5E8-x-5%5E3%2F5%5E4-x-2%5E10-x-10.jpeg "(-2)^8 X 5^3/5^4 X 2^10 X 10")
Simplifying the Expression: (-2)^8 x 5^3/5^4 x 2^10 x 10
This expression involves several exponents and multiplications. Let's break it down step-by-step to simplify it.
Understanding the Rules
- Exponents: A number raised to a power (like 2^3) means multiplying the number by itself that many times (2 x 2 x 2).
- Negative Exponents: A negative exponent means taking the reciprocal of the base raised to the positive power (e.g., 2^-3 = 1/2^3).
- Fractions with Exponents: When dividing exponents with the same base, subtract the powers (e.g., 5^3/5^4 = 5^(3-4) = 5^-1).
- Multiplication with the Same Base: When multiplying exponents with the same base, add the powers (e.g., 2^3 x 2^4 = 2^(3+4) = 2^7).
Simplifying the Expression
- Simplify (-2)^8: (-2)^8 = 256 (since an even power of a negative number results in a positive number).
- Simplify 5^3/5^4: 5^3/5^4 = 5^-1 = 1/5
- Simplify 2^10 x 10: 2^10 x 10 = 1024 x 10 = 10240
- Combine the simplified terms: 256 x (1/5) x 10240
- Calculate the final result: (256 x 10240) / 5 = 524288
Therefore, the simplified value of (-2)^8 x 5^3/5^4 x 2^10 x 10 is 524288.