Can someone explain the rules for raising a power to a power?
Please explain and give some examples. I would appreciate it if you can answer this as soon as possible.
I really need to understand it for a question, and I want to see some examples of it too.
Depends what you mean by raising a power to a power
e.g.
(3^2)^3
= (3^2)(3^2)(3^2) = (9)(9)(9) = 729
or
= 3^6 = 729
if the two exponents are at the same "horizontal level"
then you multiply the two or more exponents
(a^x)^y = a^(xy)
do not confuse that with (a^x)(a^y) = a^(x+y)
if the exponent itself is raised, you work from the top down
e.g.
3^42
= 3^16
= 43046721
Hope that helps you
Thank you Reiny, I now understand the rule or rules. You helped me a lot, and saved me some researching time. Sorry that I couldn't say thank you sooner, but I had to do something else. Thank you again, you really did help me.
Just curious how posting a question, waiting for an answer, reading it and posting a reply saved time over just opening your text to the appropriate section and reading that explanation.
Just sayin' . . .
Sure, I can explain the rules for raising a power to a power. When you raise a power to a power, you are essentially multiplying the exponents together.
To better understand this concept, let's use an example:
Let's say we have the expression (a^m)^n, where "a" is the base, "m" is the first exponent, and "n" is the second exponent.
To simplify this expression, you multiply the exponents as follows:
(a^m)^n = a^(m * n)
Here are a few examples to illustrate the concept:
Example 1:
Simplify (x^2)^3
In this case, "x" is the base, and we have two exponents: 2 and 3.
To simplify, we multiply the exponents:
(x^2)^3 = x^(2 * 3) = x^6
So, (x^2)^3 simplifies to x^6.
Example 2:
Simplify (3^4)^2
In this case, "3" is the base, and we have two exponents: 4 and 2.
Following the rule, we multiply the exponents:
(3^4)^2 = 3^(4 * 2) = 3^8
So, (3^4)^2 simplifies to 3^8.
Example 3:
Simplify (a^3)^2
In this case, "a" is the base, and we have two exponents: 3 and 2.
Using the rule, we multiply the exponents:
(a^3)^2 = a^(3 * 2) = a^6
So, (a^3)^2 simplifies to a^6.
Remember, when raising a power to a power, you multiply the exponents. This rule holds true for all real numbers and variables.