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Eduardwww [97]
3 years ago
8

Which expression is equivalent to [(3xy^-5)^3 / (x^-2y^2)^-4]^-2

Mathematics
2 answers:
True [87]3 years ago
4 0
<span>The answer is (x</span>¹⁰<span>y</span>¹⁴<span>)/729.

Explanation:
We can begin simplifying inside the innermost parentheses using the properties of exponents. The power of a power property says when you raise a power to a power, you multiply the exponents. This gives us

[(3</span>³<span>x</span>³<span>y</span>⁻¹⁵<span>)/(x</span>⁸<span>y</span>⁻⁸<span>)]</span>⁻²<span>.

Negative exponents tell us to "flip" sides of the fraction, so within the parentheses we have
[(3</span>³<span>x</span>³<span>y</span>⁸<span>)/(x</span>⁸<span>y</span>¹⁵<span>)]</span>⁻²<span>.

Using the quotient property, we subtract exponents when dividing powers, which gives us
(3</span>³<span>/x</span>⁵<span>y</span>⁷<span>)</span>⁻²<span>.

Evaluating 3</span>³<span>, we have
(27/x</span>⁵<span>y</span>⁷<span>)</span>⁻²<span>.

Using the power of a power property again, we have
27</span>⁻²<span>/x</span>⁻¹⁰<span>y</span>⁻¹⁴<span>.

Flipping the negative exponents again gives us x</span>¹⁰<span>y</span>¹⁴<span>/729.</span>
slavikrds [6]3 years ago
3 0

Answer with explanation:

The given expression is

=[\frac{(3 x y^{-5})^3}{(x^{-2}y^2)^{-4}}]^{-2}\\\\=\frac{(3 x y^{-5})^{-6}}{(x^{-2}y^2)^{8}}\\\\=\frac{(3^{-6} x^{-6} y^{30})}{(x^{-16}y^{16})}\\\\=3^{-6}\times x^{-6+16}\times y^{30-16}\\\\=\frac{x^{10}\times y^{14}}{729}

Used the following law of indices

1.[\frac{x}{y}]^m=\frac{x^m}{y^m}\\\\ 2. \frac{x^m}{x^n}=x^{m-n}\\\\ 3. \frac{1}{x^{-m}}=x^m

The given expression is equivalent to

\frac{x^{10}\times y^{14}}{729}

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David earns $8 per hour he works 40 hours each week how much does he earn in 6 weeks
dem82 [27]

Answer:

$1920

Step-by-step explanation:

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3 years ago
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5(m+4)=-2(-4-m)+3<br> help please
Degger [83]

Answer:

m = -3

Step-by-step explanation:

5m + 20 = 8 + 2m +3

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3 0
3 years ago
Old faithful in Yellowstone National Park shoots water 60 feet into the air that casts a shadow of 42 feet. What is the height o
Serhud [2]

Answer:

The height of near by tree will be 90 feet.

Step-by-step explanation:

Considering the water triangle as shown in figure a.

As the old faithful shoots water 60 feet into the air that casts a shadow of 42 feet.

Considering the tree triangle as shown in figure a. The tree triangle has a shadow 63 feet long.

Let x be the height of near by tree that cost a shadow 63 feet long.

Assuming that the triangles are similar

So,

the ratios of similar triangles will be related as:

\frac{63}{42}=\frac{x}{60}

\mathrm{Switch\:sides}

\frac{x}{60}=\frac{63}{42}

{x}=60.\frac{63}{42}

x=90 feet

Therefore, the height of near by tree will be 90 feet.

Keywords: ratio, similar triangle

Learn more about similar triangle from brainly.com/question/10161974

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3 years ago
The volume of the box below is 1.5 cubic inches. Which of the following are possible dimensions of the box.
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I’m not sure what u mean?
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3 years ago
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