1. Write z^9/z^3 in simplest form.
a. z^3
b. z^6
c. z^12
d. z^27
2. Which symbol will make the number sentence true? 6/7 ? 0/85
a. =
b. <
c. >
3. Which of the following numbers is an example of an integer?
a. 5 (square rooted)
b. 9 (square rooted)
c. 1/3
d. 0.8
PLEASE HELP ME ASAP!
What do you think the answer is for each of them?
WHen the bases are the same and you are dividing you can subtract the exponents. It is a "fast" way to do the reducing : )
z^9/z^3 = z^(9-3) = z^6
or, consider that
z^9/z^3 = (z^6*z^3)/z^3 = z^6
0/85 = 0
so, ANY positive value is greater than zero, right?
since 9 = 3^2, the square root is 3
I think if you consider the others, you will soon see that they cannot be integers.
1. A
2. C
3. A
maybe these?
ALL wrong!
And I even gave you the final answer to the first one.
Stop guessing and start thinking.
1. To simplify the expression z^9/z^3, you can use the rule of exponents that states when dividing two numbers with the same base, you subtract the exponents. In this case, z is the base and 9 is the exponent of the numerator, while 3 is the exponent of the denominator.
So, z^9/z^3 can be simplified as z^(9-3) = z^6.
Therefore, the answer is (b) z^6.
2. To determine which symbol makes the number sentence 6/7 ? 0/85 true, you need to compare the two fractions.
For fractions, the value of the fraction decreases as the denominator gets larger. So, the fraction 0/85 is smaller than 6/7.
Therefore, the correct symbol is (b) <, indicating that 6/7 is less than 0/85.
3. An integer is a whole number that can be positive, negative, or zero.
Out of the options given:
a. 5 (square rooted) is not an integer because it will likely result in an irrational number.
b. 9 (square rooted) is not an integer because it will also likely result in an irrational number.
c. 1/3 is not an integer because it is a fraction.
d. 0.8 is not an integer because it is a decimal number.
Therefore, the answer is none of the above.