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nydimaria [60]
3 years ago
7

I NEED URGENT ASSISTANCE

Mathematics
1 answer:
Nata [24]3 years ago
7 0

Answer:

<em>8 C sometimes</em>

<em>9 64x^8 y^11</em>

<em>10 c 1.28r^2/ t^9</em>

Step-by-step explanation:

<u>Algebraic Operations </u>

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:

\displaystyle \left(\frac{x^n.y^m}{z^p}\right)^q= \frac{x^{qn}.y^{qm}}{z^{qp}}

\displaystyle \frac{x^n.x^q}{x^p}= x^{n+q-p}

\displaystyle x^{-n}=\frac{1}{x^n}

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

\displaystyle 3^{-2}=\frac{1}{3^2}=\frac{1}{9}

This is a negative power resulting in a positive number

Now we pick

\displaystyle (-2)^{-3}=\frac{1}{(-2)^3}=-\frac{1}{8}

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

<em>Answer: C sometimes </em>

9 simplify(4xy^2)^3(xy)^5

(4xy^2)^3(xy)^5=4^3x^3(y^2)^3x^5y^5

=64x^3y^6x^5y^5

=64x^8y^{11}

10 simplify(2t^-3)^3(0.4r)^2

(2t^{-3})^3(0.4r)^2=2^3(t^{-3})^30.4^2r^2

=8t^{-9} 0.16 r^2

=1.28t^{-9} r^2

\displaystyle \frac{1.28 r^2}{t^9}

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