Sure, I will simplify each expression step-by-step.
a. [tex]\(-42 + (-17)\)[/tex]:
- When you add two negative numbers, you add their absolute values and keep the negative sign.
- [tex]\(-42 + (-17) = -(42 + 17) = -59\)[/tex]
b. [tex]\(8 - (-9)\)[/tex]:
- Subtracting a negative number is the same as adding its positive counterpart.
- [tex]\(8 - (-9) = 8 + 9 = 17\)[/tex]
c. [tex]\(8 \times (-9)\)[/tex]:
- Multiplying a positive number by a negative number results in a negative number.
- [tex]\(8 \times (-9) = -72\)[/tex]
d. [tex]\(-42 \div (-7)\)[/tex]:
- Dividing two negative numbers results in a positive number.
- [tex]\(-42 \div (-7) = 6.0\)[/tex]
e. [tex]\(-2 \times (-3) \times (-4)\)[/tex]:
- First, multiply two negative numbers, which gives a positive result.
- [tex]\(-2 \times (-3) = 6\)[/tex]
- Then multiply the result by a negative number, which gives a negative result.
- [tex]\(6 \times (-4) = -24\)[/tex]
f. [tex]\(-18 - 7\)[/tex]:
- Subtracting a positive number from a negative number is the same as adding the absolute value of the positive number to the absolute value of the negative number and keeping the negative sign.
- [tex]\(-18 - 7 = -(18 + 7) = -25\)[/tex]
g. [tex]\((-5)^2\)[/tex]:
- Squaring a negative number results in a positive number.
- [tex]\((-5)^2 = 25\)[/tex]
h. [tex]\(-5^2\)[/tex]:
- The exponentiation is done first, and then the negative sign is applied.
- [tex]\(5^2 = 25\)[/tex], and then apply the negative sign.
- [tex]\(-5^2 = -25\)[/tex]
i. [tex]\(\sqrt{49}\)[/tex]:
- The square root of 49 is the number that, when multiplied by itself, gives 49.
- [tex]\(\sqrt{49} = 7.0\)[/tex]
So, the simplified results for each expression are:
a. [tex]\(-59\)[/tex]
b. [tex]\(17\)[/tex]
c. [tex]\(-72\)[/tex]
d. [tex]\(6.0\)[/tex]
e. [tex]\(-24\)[/tex]
f. [tex]\(-25\)[/tex]
g. [tex]\(25\)[/tex]
h. [tex]\(-25\)[/tex]
i. [tex]\(7.0\)[/tex]
