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(-1/2)^8

less than a minute read Jun 16, 2024
(-1/2)^8

Understanding (-1/2)^8

In mathematics, exponents indicate how many times a base number is multiplied by itself. In this case, we have (-1/2)^8, which means we multiply (-1/2) by itself 8 times.

Calculating the Result

  • Step 1: Even Exponent: Notice that the exponent (8) is even. This is crucial because an even exponent applied to a negative base results in a positive answer.

  • Step 2: Individual Multiplication: We can simplify the calculation by first considering the numerator and denominator separately.

    • (-1)^8 = 1 (any negative number raised to an even power becomes positive)
    • (2)^8 = 256

  • Step 3: Combining the Results: Combining the results, we get:

    (-1/2)^8 = (-1)^8 / (2)^8 = 1 / 256

Conclusion

Therefore, (-1/2)^8 is equal to 1/256.

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