Answer:
8 C sometimes
9 64x^8 y^11
10 c 1.28r^2/ t^9
Step-by-step explanation:
Algebraic Operations
Some basic rules must be fresh in our minds when trying to simplify complex algebraic expressions. For example, the power rule respect to the product or quotient:
[tex]\displaystyle \left(\frac{x^n.y^m}{z^p}\right)^q= \frac{x^{qn}.y^{qm}}{z^{qp}}[/tex]
[tex]\displaystyle \frac{x^n.x^q}{x^p}= x^{n+q-p}[/tex]
[tex]\displaystyle x^{-n}=\frac{1}{x^n}[/tex]
Let's face the questions at hand
8. A number is raised to a negative exponent is negative?
Following the expressions recalled above, let's pick the expression
[tex]\displaystyle 3^{-2}=\frac{1}{3^2}=\frac{1}{9}[/tex]
This is a negative power resulting in a positive number
Now we pick
[tex]\displaystyle (-2)^{-3}=\frac{1}{(-2)^3}=-\frac{1}{8}[/tex]
This time, the negative power leads to a negative result, so it doesn't matter the sign of exponent to determine the sign of the result
Answer: C sometimes
9 simplify(4xy^2)^3(xy)^5
[tex](4xy^2)^3(xy)^5=4^3x^3(y^2)^3x^5y^5[/tex]
[tex]=64x^3y^6x^5y^5[/tex]
[tex]=64x^8y^{11}[/tex]
10 simplify(2t^-3)^3(0.4r)^2
[tex](2t^{-3})^3(0.4r)^2=2^3(t^{-3})^30.4^2r^2[/tex]
[tex]=8t^{-9} 0.16 r^2[/tex]
[tex]=1.28t^{-9} r^2[/tex]
[tex]\displaystyle \frac{1.28 r^2}{t^9}[/tex]
