How do I go about solving (27x^3/8y^9)^5/3? And what is the role of the numerator and denominator?

Answers

Answer 1

Answer: $\left( (27x^3)/(8y^9)\right)^ (5)/(3) \n\n\n =\left( ((3x)^3)/((2y^3)^3)\right)^ (5)/(3) \n\n\n = \frac{(3x)^{3 * (5)/(3) }}{(2y^3)^{3 * (5)/(3) }} \n\n\n =((3x)^5)/((2y^3)^(5 )) \n\n\n =(243x^5)/(32y^(15))$

Now, If the exponent was negative like you asked....

$\left( (27x^3)/(8y^9)\right)^ {-(5)/(3)} \n\n\n =\left( (8y^9)/(27x^3)\right)^ {(5)/(3)}\n\n\n =\left( ((2y^3)^3)/((3x)^3)\right)^ (5)/(3) \n\n\n = \frac{(2y^3)^{3 * (5)/(3) }}{(3x)^{3 * (5)/(3) }} \n\n\n =((2y^3)^(5 ))/((3x)^5) \n\n\n =(32y^(15))/(243x^5)$

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Select the correct answer. Gary throws a parachute toy from the roof of a building which has a height of 96 feet. The toy reaches its maximum height of 100 feet after 2 seconds, and it hits the ground after 12 seconds. Which of the following graphs represents the height of the toy?

Answers

Answer:

Step-by-step explanation:

The height needs to start at 96

Find the Value of 8 1/3

Answers

The value of $8^{(1)/(3) }$ is 2.

What are the laws of exponents?

The Laws of Exponents are:

$x^(m) .x^(n) =x^(m+n)$

$(x^(m) )/(x^(n) ) =x^(m-n)$

$(x^{^(m))n}=x^(mn)$

$(xy)^(m) =x^(m) y^(m)$

According to the given question.

We have a number in exponential form $8^{(1)/(3) }$

The above exponential number can be written as

$8^{(1)/(3) }$

$= 2^{3((1)/(3) )}$ (because $2^(3) = 8$ )

$= 2$ ( because $(3)(1)/(3) = 1$ )

Hence, the value of $8^{(1)/(3) }$ is 2.

Find out more information about laws of exponents here:

brainly.com/question/568161

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$8^{ (1)/(3) } = \sqrt[3]{8} = 2$

$8^{ (2)/(3) } = \sqrt[3]{8^2} = \sqrt[3]{64} = 4$

Use synthetic division to check -4 is a root of the polynomial expression: x^4+2x^3-9x^2-2x+8=f(x)

Answers

Hello,

........|x^4|x^3|x^2|x^1|x^0
........| 1..|.2...|.-9.|.-2.|.8
x=-3.| ....|.-4..|.8..|.4..|.-8
........| 1..|.-2..|.-1.|..2.|.0

x^4+2x^3-9x^2-2x+8=(x+3)(x^3-2x^2-x+2)+0
-4 is a root of the polynomial expression.

Which of the following expressions represents 24C12?A) 12!/24!
B 24!/24!
C) 24!/ 12!•12!
D) 24!/12!