%5E2-without-exponents.jpeg "(a^4)^2 Without Exponents")
Understanding (a^4)^2 without Exponents
The expression (a^4)^2 might seem intimidating at first, but it's actually quite straightforward to understand without using exponents. Let's break it down:
What does (a^4)^2 mean?
- a^4 means multiplying 'a' by itself four times: a * a * a * a.
- (a^4)^2 means squaring the result of a^4, or multiplying it by itself: (a * a * a * a) * (a * a * a * a).
Expanding the Expression
To get rid of the exponents, we can simply write out the multiplication:
(a * a * a * a) * (a * a * a * a) = a * a * a * a * a * a * a * a
Simplifying the Result
We now have 'a' multiplied by itself eight times. This can be expressed as:
a^8
Conclusion
Therefore, (a^4)^2 is equivalent to a^8 without using exponents. This process demonstrates the fundamental principle of exponent rules: when raising a power to another power, you multiply the exponents.