For questions 3 and 4, simplify each expression.
1. 4^4/4^6
-16
16
1/16 <-----------------
-1/16
2. 5^0
0 <-------------
5
1
–5
1 right
2. anything to zero power is 1
Well, for question 3, the expression 4^4/4^6 can be simplified by using the rules of exponents. When you have the same base raised to different exponents and they are divided, you can subtract the exponents. In this case, 4^4 means four raised to the fourth power, which is 4 * 4 * 4 * 4. Similarly, 4^6 means four raised to the sixth power, which is 4 * 4 * 4 * 4 * 4 * 4. So when you divide these two expressions, you can subtract the exponents, which gives you 4^4/4^6 = 1/4^(6-4) = 1/4^2 = 1/16. So the answer is 1/16.
And for question 4, the expression 5^0 can also be simplified using the rules of exponents. Any number raised to the power of zero is always equal to 1. So 5^0 = 1. Therefore, the answer is 1.
I hope that lightened the mood a bit!
For question 3, to simplify the expression 4^4/4^6, we can use the rule that states a^m/a^n = a^(m-n). In this case, we have 4^4/4^6, which can be simplified to 4^(4-6) = 4^(-2).
To further simplify, we can use the rule that states a^(-n) = 1/a^n. So, 4^(-2) = 1/4^2 = 1/16.
Therefore, the simplified expression is 1/16.
To simplify an expression, you typically use the rules of exponents.
For the first question, 4^4/4^6, you can simplify it by subtracting the exponents since the base is the same. That means you have (4^4)/(4^6) = 4^(4-6) = 4^-2.
Now, to simplify this further, you can remember that any nonzero number raised to the power of -n is equal to 1 divided by that number raised to the power of n. So, 4^-2 is equal to 1/(4^2), which is 1/16.
Therefore, the answer to the first question is 1/16.
For the second question, 5^0, any number raised to the power of 0 is equal to 1, except when the base is 0 itself. In this case, the base is 5, so 5^0 is equal to 1.
Therefore, the answer to the second question is 1.