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1 year ago

Apply Laws of Exponents to write an equivalent expression. (3y)-4. (2z)-4

Mathematics

1 answer:

Stels [109]1 year ago

4 0

After Applying Laws of Exponents we can write as $(6yz)^{-4}$

<h3>What is law of exponents ?</h3>

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

<h3>How are powers of powers multiplied?</h3>

Exponents with distinct bases and the same powers can be multiplied by multiplying the bases and writing the power outside of the brackets.

$a^{n}$ . $b^{n}$ = $(a.b)^{n}$

= $3y^{-4}$ . $2z^{-4}$

= $(6yz)^{-4}$

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Write an equation of the line that passes through (2,−5) and is parallel to the line 2y=3x+10

LenaWriter [7]

Step-by-step explanation:

Divide two on both sides to get rid of it and the make the equation in the form y = mx + c

$\frac{2}{2} y = \frac{3}{2} x + \frac{10}{2}$

y = 3/2x + 5

since both lines are parallel they must have the same gradient which is 3/2

y = 3/2x + c

All you have to do now is to replace x and y with (2, -5) to find c

x = 2

y = -5

-5 = 3/2 × 2 + c

-5 = 3 + c

c = -5-3

c = -8

$y = \frac{3}{2} x - 8$

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2 years ago

A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.2. What is the width of the cake pan?

Maru [420]

<span>the width of the cake pan can be found with the following formula
area = W x L=</span>432 in.2<span>
but L= 4/3W
so we have </span>
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3 years ago

Assume you are given two right triangle with congruent hypotenuses and wish to show that they are congruent

uysha [10]

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Evaluate the cosine if the angle of rotation which contains the point (9, -3) on its terminal side

Liono4ka [1.6K]

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$\bf (\stackrel{x}{9}~~,~~\stackrel{y}{-3})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{9^2+(-3)^2}\implies c=\sqrt{81+9}\implies c=\sqrt{90} \\\\[-0.35em] ~\dotfill$

$\bf cos(\theta )=\cfrac{\stackrel{adjacent}{9}}{\stackrel{hypotenuse}{\sqrt{90}}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{9}{\sqrt{90}}\cdot \cfrac{\sqrt{90}}{\sqrt{90}}\implies \cfrac{9\sqrt{90}}{90}}\implies \cfrac{\sqrt{90}}{10}\implies \cfrac{3\sqrt{10}}{10}$

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