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ss7ja [257]
3 years ago
12

Simplify completely. (w^15/w^5)^4 HELP PLEASE

Mathematics
1 answer:
Umnica [9.8K]3 years ago
8 0

Answer:

w^{40}

Step-by-step explanation:

To simplify recall exponent rules:

1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.

2. When we multiply terms with the same bases, we add exponents.

3. When we divide terms with the same bases, we subtract exponents.

4. When we have a base to the exponent of 0, it is 1.

5. A negative exponent creates a fraction.

6. When we raise an exponent to an exponent, we multiply exponents.

7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.

We will use these rules to simplify.

Use rule #3 to simplify inside the parenthesis first.

\frac{w^{15}}{w^5}  = w^{10}

Now simplify the exponent of 4 using rule 6.

(w^{10})^4 = w^{40}


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Answer:

= $3,888.89

Step-by-step explanation:

First, calculate the money multiplier(MM); which is the amount of money that is generated by the banks for each dollar of reserve. In this case, it describes how a deposited amount increases the total supply of money.

Money Multiplier = 1 / reserve ratio

Reserve ratio = 9% or 0.09

Therefore, money multiplier = 1/0.09 = 11.1111

Next, use the reserve ratio to calculate the amount of increase in money supply;

= 11.1111 * $350

= $3,888.89

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Step-by-step explanation:

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3 years ago
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Read 2 more answers
Solve: 1. 1/6y− 1/2 =3− 1/2y 2. 4x+1/15 = 2x/10
kogti [31]

<u>Answer:</u>

<em>First Equation → </em><u><em>y = 21/4</em></u>

<em>Second Equation → </em><u><em>x = -1/57</em></u>

<u />

<u>Explanation:</u>

<em>solving equation #1</em>

<em></em>

step 1 - simplify

<em></em>

\displaystyle\frac{1}{6}y - \displaystyle\frac{1}{2} = 3 - \displaystyle\frac{1}{2}y\\\\\displaystyle\frac{1}{6}* \displaystyle\frac{y}{1}  - \displaystyle\frac{1}{2} = 3 - \displaystyle\frac{1}{2}* \displaystyle\frac{y}{1}\\\\\displaystyle\frac{y}{6} - \displaystyle\frac{1}{2} = 3 - \displaystyle\frac{y}{2}

step 3 - multiply each side of the equation by six

\displaystyle\frac{y}{6} - \displaystyle\frac{1}{2} = 3 - \displaystyle\frac{y}{2}\\\\\displaystyle\frac{y}{6} * \displaystyle\frac{6}{1}- \displaystyle\frac{1}{2} * \displaystyle\frac{6}{1}= \displaystyle\frac{3}{1} *\displaystyle\frac{6}{1} - \displaystyle\frac{y}{2}* \displaystyle\frac{6}{1}\\\\y - 3 = 18 - 3y

step 4 - add three to both sides of the equation.

y - 3 = 18 - 3y\\\\y-3+3=18+3-3y\\\\y = -3y+21

step 5 - add three y to both sides of the equation.

y = -3y+21\\\\y+3y = -3y+3y+21\\\\y+3y=21

step 6 - simplify

y+3y=21\\\\4y=21

step 7 - divide both sides of the equation by four

4y=21\\\\\displaystyle\frac{4y}{4} = \displaystyle\frac{21}{4}\\ \\y = \displaystyle\frac{21}{4}

Therefore, the solution to the first given equation is <u><em>y = 21/4 </em></u><em>or y = 5.25.</em>

<u><em /></u>

<em>solving equation #2</em>

<em />

step 1 - simplify.

4x + \displaystyle\frac{1}{15}  = \displaystyle\frac{2x}{10} \\\\4x + \displaystyle\frac{1}{15}  = 2*\displaystyle\frac{x}{10}\\\\4x+\displaystyle\frac{1}{15}  = \displaystyle\frac{x}{5}

step 2 - multiply each side of the equation by five.

4x+\displaystyle\frac{1}{15}  = \displaystyle\frac{x}{5}\\\\\displaystyle\frac{4x}{1}* \displaystyle\frac{5}{1}  +\displaystyle\frac{1}{15} * \displaystyle\frac{5}{1}  = \displaystyle\frac{x}{5}* \displaystyle\frac{5}{1} \\\\20x + \displaystyle\frac{1}{3} = x

step 3 - subtract twenty x from each side of the equation.

20x + \displaystyle\frac{1}{3} = x \\\\20x -20x+ \displaystyle\frac{1}{3} = x -20x\\\\\displaystyle\frac{1}{3} = -19x

step 4 - divide each side of the equation by negative nineteen.

\displaystyle\frac{1}{3} = -19x\\\\\displaystyle\frac{\displaystyle\frac{1}{3} }{-19} = \displaystyle\frac{-19x}{-19} \\\\-\displaystyle\frac{1}{57} = x

step 5 - switch

-\displaystyle\frac{1}{57}  =x\\\\x = -\displaystyle\frac{1}{57}

Therefore, the solution to the second equation is <em><u>x = -1/57.</u></em>

5 0
3 years ago
A random sample of 8888 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 278278. Thi
crimeas [40]

Answer:

Step-by-step explanation:

Given that sample size n = 88, for eight grade students

scores on a national mathematics assessment test has a mean score of 278. This test result prompts a state school administrator to declare that

x bar >270

H_0: xbar = 270\\H_a: x bar >270

(One tailed test at 15% sign level)

Since sigma, population sd is known and sample size is large we use z test

Std error = \frac{\sigma}{\sqrt{n} } =4.051

Mean difference 278-270=8

Z statistic = \frac{8}{4.051} =1.975

p value = 0.024

Since p <alpha, the administrator's declaration is correct.

3 0
3 years ago
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