<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>
Answer:
either 2^8/3^8 or 256/6561
Step-by-step explanation:
looked it up on Symbolab
It's always easier to understand a concept by looking at specific examples with pictures, so I suggest looking at the dilation examples below first...before you try to internalize the steps listed below and that explain the general formula for dilating a point with coordinates of (2,4) by a scale factor of <span><span>12</span><span>12</span></span>.
<span><span>1) multiply both coordinates by scale factor<span>(<span><span>2⋅<span>12</span>,4⋅<span>12</span></span><span>2⋅<span>12</span>,4⋅<span>12</span></span></span>)</span></span><span>2)
2. Simplify(1,2)</span><span>3)
3. Graph(if required)<span> </span></span></span>
A, D and E are correct
given ( x - 4 ) is a factor then x = 4 is a root
the remainder on division by (x - 4 ) = 0 as indicated by the 0 on the right side of the quotient
(x - 4 ) is a factor of 3x² - 13x + 4 → A
the number 4is a root of f(x) = 3x² - 13x + 4 → D ( explained above )
thus 3x² - 13x + 4 ÷ (x - 4 ) = 3x - 1 → E
the quotient line 3 - 1 0
3 and - 1 are the coefficients of the linear quotient and 0 is the remainder
Answer:
<u />
General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]:
Special Limit Rule [L’Hopital’s Rule]:
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]:
![\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%20%2B%20g%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D)
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given limit</em>.
<u>Step 2: Find Limit</u>
Let's start out by <em>directly</em> evaluating the limit:
- [Limit] Apply Limit Rule [Variable Direct Substitution]:
- Evaluate:
When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:
- [Limit] Apply Limit Rule [L' Hopital's Rule]:
- [Limit] Differentiate [Derivative Rules and Properties]:
- [Limit] Apply Limit Rule [Variable Direct Substitution]:
- Evaluate:
∴ we have <em>evaluated</em> the given limit.
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Learn more about limits: brainly.com/question/27807253
Learn more about Calculus: brainly.com/question/27805589
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
