Simplify this expression: 19 – (–8) – (–14) = ? A. –7 B. –3 C. 41 D. 25

1 answer:

8 0

Let's do it step by step. In the first step eliminate the two parenthesis, for which you need to use the rule of multiplication of signs: the multiplication of two equal signs leads to positive sign, the multiplication of two different signs leads to negative sign. So -(-8) = +8 and -(-14) = +14. and 19 -(-8) - (-14) - 19 + 8 + 14 = 41. The answer is the option C. 41.

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Simplify (-3c^-3w^5)^3 A -9w^8 B. -27cw^8 C. w^15/27c^9 D.-27w^15/c^9

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$\large\boxed{D.\ \dfrac{-27w^{15}}{c^9}}$

Step-by-step explanation:

$(-3c^{-3}w^5)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(-3)^3(c^{-3})^3(w^5)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=-27c^{-3\cdot3}w^{5\cdot3}=-27c^{-9}w^{15}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=-27\left(\dfrac{1}{c^9}\right)w^{15}=\dfrac{-27w^{15}}{c^9}$