How are <8 and <4 related

Reduce the following fraction: -36x^4y^4z^5/-12x^6y^3z

Evgesh-ka [11]

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\
-------------------------------\\\\$

$\bf \cfrac{-36x^4y^4z^5}{-12x^6y^3z}\quad 
\begin{cases}
36=2\cdot 2\cdot 3\cdot 3\\
12=2\cdot 2\cdot 3
\end{cases}\implies \cfrac{-36}{-12}\cdot \cfrac{x^4y^4z^5}{x^6y^3z^1}
\\\\\\
\cfrac{\underline{-2\cdot 2\cdot 3}\cdot 3}{\underline{-2\cdot 2\cdot 3}}\cdot \cfrac{x^4y^4z^5x^{-6}y^{-3}z^{-1}}{1}\implies \cfrac{3}{1}\cdot 
\cfrac{x^4x^{-6}y^4y^{-3}z^5z^{-1}}{1}$

$\bf \cfrac{3}{1}\cdot \cfrac{x^{4-6}y^{4-3}z^{5-1}}{1}\implies 
\cfrac{3}{1}\cdot\cfrac{x^{-2}y^{1}z^4}{1}\implies 
\cfrac{3x^{-2}yz^4}{1}\implies \cfrac{3yz^4}{x^2}$

6 0

3 years ago

Complete the table, for the following investments, which shows the performance (interest and balance) over a 5-year period.

sergiy2304 [10]

Answer:

After 5 years of investment, Suzanne will have $ 4,400 in her account, while Derek will have $ 4,416.32 in his account.

Step-by-step explanation:

Since Suzanne deposits $ 4000 in an account that earns simple interest at an annual rate of 2%, and Derek deposits $ 4000 in an account that earns compound interest at an annual rate of 2% and is compounded annually., Both for a period of 5 years, to determine how much money each one will have in their account after 5 years, the following calculation must be made:

Suzanne:

((4,000 x 0.02) x 5) + 4,000 = X

(80 x 5) + 4,000 = X

400 + 4,000 = X

4,400 = X

Derek:

4,000 x (1 + 0.02 / 1) ^ 5x1 = X

4,000 x 1.02 ^ 5 = X

4,416.32 = X

Thus, after 5 years of investment, Suzanne will have $ 4,400 in her account, while Derek will have $ 4,416.32 in her account.

5 0

3 years ago

A puppy is on sale at a pet store for $432, marked down 10% from an original selling price of $480. If the markup from cost

Ahat [919]

432 x 0.1 = 43.2
432-43.2= 388.8
Mark up
388.8 + 72 = 460.8

4 0

3 years ago

Thirty-three students went out for junior high football. How many ways can the coach create a lineup of 11 players?

WITCHER [35]

Only 3 ways because 33 divided by 11 is 3.

7 0

4 years ago

Read 2 more answers

Which expressions are equivalent to 6 (–x) 2x (–7) 2x? Check all that apply. X x 6 – 7 x 2x 2 x 3 – x 2x – 4 2x x – 1 x 1.

qaws [65]

Equivalent expression is the expression which is equal to the original equation but the way of representation is different. The equivalent expression of the given expression are,

$x+x+6-7+x$

$3-x+2x-4+2x=3x-1$

Given information

The given expression in the problem is,

$6+(-x)+2x+(-7)+2x$

<h3>Equivalent expression</h3>

Equivalent expression is the expression which is equal to the original equation but the way of representation is different.

The given equation is,

$6+(-x)+2x+(-7)+2x$

As the product of the negative and positive is negative. Thus solve the equation by opening the bracket.

$6+(-x)+2x+(-7)+2x=6-x+2x-7+2x\\
6+(-x)+2x+(-7)+2x=-x+2x+2x+6-7\\
6+(-x)+2x+(-7)+2x=3x-1$

Check all the option,

1) The expression given in the option 1 is,

$x+x+6-7+x$

Solve it further,

$x+x+6-7+x=x+x+x+6-7\\
x+x+6-7+x=3x-1\\$

The result is equal to the result of the given expression. Thus the expression of the option 1 is equivalent to the expression given in the problem.

2) The expression given in the option 2 is,

$2x+2+x$

Solve it further,

$2x+2+x=2x+x+2\\2x+2+x=3x+2$

The result is not equal to the result of the given expression. Thus the expression of the option 2 is not equivalent to the expression given in the problem.

3) The expression given in the option 3 is,

$3-x+2x-4+2x$

Solve it further,

$3-x+2x-4+2x=3x-1$

The result is equal to the result of the given expression. Thus the expression of the option 3 is equivalent to the expression given in the problem.