- #1
jamesd2008
- 64
- 0
What is the result of a number raised to the power of the number raised to a power.
I.e. 2^2^2?
I.e. 2^2^2?
What does it mean if I raise a power to the power etc?
In summary, raising a power to another power means multiplying the number by itself the number of times indicated by the second power. To solve expressions with powers, use exponent rules such as multiplying and dividing powers with the same base. Raising a power to a power is equivalent to multiplying exponents, while multiplying powers involves using the multiplication operation. Negative numbers can be raised to a power, but the result may be positive or negative depending on the power. Parentheses should be used when raising a power to a power in expressions involving multiple operations to ensure the correct order of operations is followed.
- #2
Mark44
Mentor
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This expression is evaluated from right to left, as if parentheses were placed like so:
2^(2^2) = 2^4 = 16.
For this problem, the order isn't important, since (2^2)^2 = 4^2, also equals 16. For other problems with different numbers, thought, you can get different results.
For example, 5^2^3 = 5^(2^8) = 5^8 = 390625.
If you evaluate in the wrong order, you get (5^2)^3 = 25^3 = 15625.
2^(2^2) = 2^4 = 16.
For this problem, the order isn't important, since (2^2)^2 = 4^2, also equals 16. For other problems with different numbers, thought, you can get different results.
For example, 5^2^3 = 5^(2^8) = 5^8 = 390625.
If you evaluate in the wrong order, you get (5^2)^3 = 25^3 = 15625.
- #3
jamesd2008
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- 0
Thats great thanks
- #4
DaveC426913
Gold Member
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Too soon to introduce him to "[URL Number[/URL]? 
Last edited by a moderator:
- #5
Mark44
Mentor
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Might be!
1. What does it mean to raise a power to another power?
When raising a number to another power, it means to multiply that number by itself the number of times indicated by the second power. For example, 2 raised to the power of 3 would be 2 x 2 x 2 = 8.
2. How do I solve expressions with powers?
To solve expressions with powers, you can use the exponent rules to simplify the expression. These rules include multiplying powers with the same base, dividing powers with the same base, and raising a power to another power.
3. What is the difference between raising a power to a power and multiplying powers?
Raising a power to a power involves exponentiation, while multiplying powers involves using the multiplication operation. In other words, raising a power to a power is equivalent to multiplying exponents, while multiplying powers is equivalent to multiplying the base numbers.
4. Can I raise a negative number to a power?
Yes, you can raise a negative number to a power. However, the result may be positive or negative depending on the power. If the power is an even number, the result will be positive. If the power is an odd number, the result will be negative.
5. How do I know when to use parentheses when raising a power to a power?
It is important to use parentheses when raising a power to a power if the expression involves multiple operations. This ensures that the order of operations is followed correctly. Otherwise, the result may be incorrect.
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