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emmasim [6.3K]
3 years ago
12

Simplify each expression. Use positive exponents. A^4b^-3 ab^-2

Mathematics
2 answers:
Leni [432]3 years ago
8 0
\dfrac{a^4b^{-3}}{ab ^{-2}}=\dfrac{a^4}{a^1}\cdot\dfrac{b^{-3}}{b^{-2}}=a^{4-1}\cdot b^{-3-(-2)}=a^3\cdot b^{-3+2}=a^3\cdot b^{-1}=a^3\cdot\dfrac{1}{b}=\\\\\\=\boxed{\dfrac{a^3}{b}}
choli [55]3 years ago
6 0
\dfrac{a^4b^{-3}}{ab^{-2}}

= {a^{4-1}b^{-3+2}}

= {a^{3}b^{-1}}

= \dfrac{a^3}{b}


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Find the equation of a line that is perpendicular to y = 3x – 5 and passes through the point (1, -3).
Svetradugi [14.3K]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y = \stackrel{\stackrel{m}{\downarrow }}{3}x-5

well then therefore

\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}

so we're really looking for the equation of a line with slope of -1/3 and that passes through (1, -3 )

(\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-\cfrac{1}{3}}(x-\stackrel{x_1}{1})\implies y+3=-\cfrac{1}{3}x+\cfrac{1}{3} \\\\\\ y=-\cfrac{1}{3}x+\cfrac{1}{3}-3\implies y=-\cfrac{1}{3}x-\cfrac{8}{3}

6 0
2 years ago
What is the greatest common factor of 45x^3, 24x^2, and 16x?
Phoenix [80]

Answer:

\huge\boxed{\sf GCF = x}

Step-by-step explanation:

<u>Firstly we'll factorize the terms:</u>

45x³ = 3 * 3 * 5 * x * x * x

24x² = 2 * 2 * 2 * 3 * x * x

16x = 2 * 2 * 2 * 2 * x

<u>The factor which is common in all three terms is:</u>

= x

Hence GCF = x

\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
8 0
2 years ago
6+6y=-30 solve for y​
kakasveta [241]

Answer:

y = -6

Step-by-step explanation:

6 + 6y = -30

6y = -30 - 6

6y = -36

y = -6

7 0
2 years ago
-5y-y=??? Algebra. Confused. Help.
MrRa [10]

Answer:

-6y

Step-by-step explanation:

-5y-y=-6y

8 0
2 years ago
Read 2 more answers
Equations must have combining like terms answer must be x=12
AnnyKZ [126]

Answer:suppose

5x+x=72

6x=72

x=72/6

x=12

8 0
3 years ago
Read 2 more answers
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