%5E4-without-exponents.jpeg "(b^2)^4 Without Exponents")
Understanding (b^2)^4 without Exponents
This expression, (b^2)^4, might look intimidating at first, but it's actually quite simple to understand without relying on exponents. Let's break it down:
What does (b^2) mean?
- b^2 means b multiplied by itself: b * b
What does (b^2)^4 mean?
- (b^2)^4 means (b^2) multiplied by itself four times: (b^2) * (b^2) * (b^2) * (b^2)
Expanding the expression
Now let's replace each (b^2) with its expanded form (b * b):
(b * b) * (b * b) * (b * b) * (b * b)
The final result
Counting the total number of 'b's being multiplied together, we get:
b * b * b * b * b * b * b * b
This can be written more concisely as b⁸.
Conclusion
Therefore, (b^2)^4 is equivalent to b multiplied by itself eight times, or b⁸. This demonstrates that even complex expressions involving exponents can be understood through basic multiplication.