Ask question

Ask question

All categories

3 years ago

6

Simplify the expression. Write your answer using only positive exponents. Evaluate any numerical powers.

1 answer:

gtnhenbr [62]3 years ago

5 0

Answer:

9x⁵

Step-by-step explanation:

<u>Use properties of exponents:</u>

<u /> $a^{b} a^{c} = a^{b+c}$ , $(a^{b} ^)^{c} = a^{bc}$ , $1/a^{-b} = a^{b}$

<u>Simplify the given expression:</u>

3⁴⋅x⋅(3/x²)⁻² =
3⁴·x·(3x⁻²)⁻² =
3⁴·x·(3⁻²)(x⁻²ˣ⁻²) =
3⁴⁻²·x¹⁺4 =
3²·x⁵ =
9x⁵

You might be interested in

2x-5y+5z=-10<br> 5x-4y+3z=-19<br> X-y+5z=17

yarga [219]

Answer:

x = -125/71 , y = 448/71 , z = 356/71

Step-by-step explanation:

Solve the following system:

{2 x - 5 y + 5 z = -10 | (equation 1)

5 x - 4 y + 3 z = -19 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Swap equation 1 with equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

2 x - 5 y + 5 z = -10 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Subtract 2/5 × (equation 1) from equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - (17 y)/5 + (19 z)/5 = (-12)/5 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Multiply equation 2 by 5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Subtract 1/5 × (equation 1) from equation 3:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x - y/5 + (22 z)/5 = 104/5 | (equation 3)

Multiply equation 3 by 5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x - y + 22 z = 104 | (equation 3)

Subtract 1/17 × (equation 2) from equation 3:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+(355 z)/17 = 1780/17 | (equation 3)

Multiply equation 3 by 17/5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+71 z = 356 | (equation 3)

Divide equation 3 by 71:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Subtract 19 × (equation 3) from equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y+0 z = (-7616)/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Divide equation 2 by -17:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Add 4 × (equation 2) to equation 1:

{5 x + 0 y+3 z = 443/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Subtract 3 × (equation 3) from equation 1:

{5 x+0 y+0 z = (-625)/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Divide equation 1 by 5:

{x+0 y+0 z = (-125)/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Collect results:

Answer: {x = -125/71 , y = 448/71 , z = 356/71

5 0

3 years ago

What is the conditional probability that exactly four heads appear when a fair coin is flipped five times

cestrela7 [59]

Answer:

5/32

Step-by-step explanation:

If a coin if flipped five times with four heads, then it has exactly one tail. The number of way to arrange four heads and one tail are as follows:

T H H H H

H T H H H

H H T H H

H H H T H

H H H H T

Essentially, there are five way because there are five "positions" where the tail could be.

Then, you need to find the total amount of possibilities for flipping a coin five times. Every time you flip it, there are two possibilities- heads and tails. Therefore, for five flips, the total amount of possibilities is

2x2x2x2x2 = 32

You know that

probability= # of desired outcome

----------------------------------

# of total outcomes

So the probablity is 5/32.

8 0

3 years ago

(V. An aeroplane is flying parallel to the Earth's surface at a speed of 175 m/sec and at a height of 600 m. The angle of elevat

GREYUIT [131]

dot on top of earth = plane position at the time of observation (right one when 37°, left one 53°)

then the geometry is zoomed on the left side

4 0

3 years ago

X=3y + 1<br> 2x + 4y =12

Alika [10]

Answer:

the solution is (4, 1).

Step-by-step explanation:

The goal here is to "solve this system of linear equations." You need to share that along with the equations.

We can begin the solution by substituting 3y + 1 for x in the second equation:

2(3y + 1) + 4y = 12

Performing the multiplication, we get 6y + 2 + 4y = 12, or 10y = 10.

Then y must be 1.

Substituting 1 for y in the first equation, we get x = 3(1) + 1 = 4

Thus, the solution is (4, 1).

4 0

3 years ago

Rewrite the following equation in slope-intercept form. 6x − 14y = -3 Write your answer using integers, proper fractions, and im

Alex17521 [72]

Answer:
y = (3/7) x + (3/14)

Explanation:
The slope-intercept form has the following formula:
y = mx + c
where:
m is the slope
c is the y-intercept

The given is:
6x - 14y = -3

To get in the slope-intercept form, we need to isolate the y as follows:
6x - 14y = -3
14y = 6x + 3
y = (6/14)x + (3/14)
y = (3/7) x + (3/14)

Hope this helps :)

7 0

3 years ago

Read 2 more answers