%5E2-without-exponents.jpeg "(p^4)^2 Without Exponents")
Understanding (p^4)^2 Without Exponents
The expression (p^4)^2 can seem intimidating at first glance, but it's actually quite straightforward to understand without relying on exponents. Let's break it down:
Understanding the Basics
- Exponent: An exponent indicates how many times a base number is multiplied by itself. For example, p^4 means p * p * p * p.
- Power of a Power: When we have an exponent raised to another exponent, like (p^4)^2, it means we're raising the entire result of the first exponent to the second exponent.
Breaking Down (p^4)^2
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Inner Exponent: First, we tackle the inner exponent, p^4. This means p multiplied by itself four times: p * p * p * p.
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Outer Exponent: Now, we take the result of p^4, which is p * p * p * p, and raise it to the power of 2. This means multiplying the entire expression by itself: (p * p * p * p) * (p * p * p * p).
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Simplifying: Expanding the multiplication, we get: p * p * p * p * p * p * p * p.
Final Result
Ultimately, (p^4)^2, without exponents, is simply p multiplied by itself eight times. This can be written as p * p * p * p * p * p * p * p.
Key Takeaway
Understanding the concept of exponents allows us to simplify complex expressions like (p^4)^2 into a more manageable form. By breaking it down step by step, we can see that it's just a matter of repeated multiplication.