If bob does his homework then George dose'nt get candy
The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )² is
.
Hence, option B is the correct answer.
<h3>What is the simplified form of the expression?</h3>
Given the expression;
( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²
First, we use the properties of exponents.
( 2⁻²ˣ⁻³ × 3⁴ˣ⁻³ ) × ( 2⁻³ˣ² × 3²ˣ² )
( 2⁶ × 3⁻¹² ) × ( 2⁻⁶ × 3⁴ )
We take out the parentheses, such that;
2⁶ × 2⁻⁶ × 3⁻¹² × 3⁴
<em>Note that: </em>2⁶ × 2⁻⁶ = 1, as ![2^6*2^{-6}=2^{6+(-6)}=2^0=1](https://tex.z-dn.net/?f=2%5E6%2A2%5E%7B-6%7D%3D2%5E%7B6%2B%28-6%29%7D%3D2%5E0%3D1)
Hence, we have
1 × 3⁻¹² × 3⁴
3⁻¹²⁺4
3⁻⁸
Next, we express with positive exponent
![\frac{1}{3^8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%5E8%7D)
The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )² is
.
Hence, option B is the correct answer.
Learn more on how to simplify expressions here: brainly.com/question/403991
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Answer:
3(4x - 1)(2x + 3)
Step-by-step explanation:
Rearrange the equation into standard form
Subtract 9 - 30x from both sides
24x² + 30x - 9 = 0 ← in standard form
Take out 3 as a common factor
3(8x² + 10x - 3) = 0 ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term
product = 8 × - 3 = - 24, sum = 10
The factors are - 2 and + 12
Use these factors to replace the x- term, that is
8x² - 2x + 12x - 3 ( factor the first/second and third/fourth terms )
2x(4x - 1) + 3(4x - 1) ← take out the common factor (4x - 1)
(4x - 1)(2x + 3)
24x² + 30x - 9 = 3(4x - 1)(2x + 3) ← in factored form
The change in the water vapors is modeled by the polynomial function c(x). In order to find the x-intercepts of a polynomial we set it equal to zero and solve for the values of x. The resulting values of x are the x-intercepts of the polynomial.
Once we have the x-intercepts we know the points where the graph crosses the x-axes. From the degree of the polynomial we can visualize the end behavior of the graph and using the values of maxima and minima a rough sketch can be plotted.
Let the polynomial function be c(x) = x
² -7x + 10
To find the x-intercepts we set the polynomial equal to zero and solve for x as shown below:
x
² -7x + 10 = 0
Factorizing the middle term, we get:
x
² - 2x - 5x + 10 = 0
x(x - 2) - 5(x - 2) =0
(x - 2)(x - 5)=0
x - 2 = 0 ⇒ x=2
x - 5 = 0 ⇒ x=5
Thus the x-intercept of our polynomial are 2 and 5. Since the polynomial is of degree 2 and has positive leading coefficient, its shape will be a parabola opening in upward direction. The graph will have a minimum point but no maximum if the domain is not specified. The minimum points occurs at the midpoint of the two x-intercepts. So the minimum point will occur at x=3.5. Using x=3.5 the value of the minimum point can be found. Using all this data a rough sketch of the polynomial can be constructed. The figure attached below shows the graph of our polynomial.