%5E4-without-exponents.jpeg "(p^2)^4 Without Exponents")
Understanding (p^2)^4 without Exponents
The expression (p^2)^4 might seem intimidating at first, especially if you're not comfortable working with exponents. But let's break it down step by step.
What Does (p^2)^4 Mean?
The expression (p^2)^4 essentially means we're multiplying p^2 by itself four times:
(p^2)^4 = p^2 * p^2 * p^2 * p^2
Expanding the Expression
To get rid of the exponents, we can expand each p^2:
- p^2 = p * p
Substituting this back into our original expression:
(p^2)^4 = (p * p) * (p * p) * (p * p) * (p * p)
Now, we have a series of multiplications.
Simplifying the Expression
By multiplying all the p's together, we get:
(p^2)^4 = p * p * p * p * p * p * p * p
Finally, we can write this as:
**(p^2)^4 = ** p^8
Key Takeaway
The expression (p^2)^4, when expanded and simplified, is equivalent to p^8. This illustrates a fundamental rule of exponents: when raising a power to another power, you multiply the exponents.