(1/8)^2x Base 2

Jasonbradley

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Jun 16, 2024

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Understanding (1/8)^2x Base 2

This article will explore the expression (1/8)^2x in base 2, breaking down its components and demonstrating how to simplify it.

Understanding the Base

The expression (1/8)^2x is written in base 2, meaning we're dealing with powers of two. It's important to remember that:

• 1/8 is equivalent to 2^-3
• The entire expression is raised to the power of 2x.

Simplifying the Expression

1. Substitute the base: We can substitute 2^-3 for 1/8: (2^-3)^2x
2. Apply the power of a power rule: When raising a power to another power, we multiply the exponents: 2^(-3 * 2x)
3. Simplify the exponent:
   2^(-6x)

Conclusion

Therefore, (1/8)^2x base 2 simplifies to 2^(-6x). This simplification helps us work with the expression more easily, especially when solving equations or performing other mathematical operations.

Key Takeaways:

• Understanding base conversions is crucial for working with exponents.
• Simplifying expressions using exponent rules can make them easier to manipulate.
• The expression (1/8)^2x can be expressed as 2^(-6x) in base 2.