All categories

3 years ago

Prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1

Mathematics

1 answer:

andreev551 [17]3 years ago

8 0

Answer:

First write them in positive exponent form

(16/81)¾ × [ (9/25)^3/2 ÷ (2/5)³ ]

(2⁴×¾)/ (3⁴×¾) × [ (3² × ^3/2) / (5² ×^3/2) ÷ 2³/5³)

Simplify the terms

2³/3³ × ( 3³ / 5³ ÷ 2³/5³)

Solve the terms in the bracket

2³/3³ × (3³/5³×5³/2³)

You will get

2³/3³ × 3³/2³ = 1

They will cancel each other so the answer will be 1

Hope this helps.

You might be interested in

A particular car is said to depreciate 15% a year. If the new car was valued at $20,000, what will it be worth after 6 years?

Margarita [4]

Answer:7542.99 dollars

Step-by-step explanation:20000 (base price) x (1 - .15) (depreciation value) to the 6th power

20000(0.85)⁶

7 0

3 years ago

Alex is mailing an envelope that weighs 0.346 pounds.What is the weight of the envelope rounded to the nearest hundredth

tangare [24]

The hundredth place is the second number on the right side of the decimal place. In this case, it is the 4 in the number you listed above.

Rounding is simple, once you get the hang of it. :)

To round on the right side of the decimal, you look at the number to the right of the number. If the number to the right of that number is five or over, the number rounds up. But, if it is less than five, the number remains the same. Either way, the number/s to the right of the one you are rounding disappear after you are done.

So let's look at your equation. The number you wish to round up- the hundredths place is the number 4. The number to the right of the four is a six. Since that is five or over, we round up. So the number would end up being .35 pounds to the nearest hundredth.

Thanks for the opportunity to answer your question and I hope I helped! If I answered your question, please consider nominating me for the brainliest answer, friending me, or even leaving a comment on my profile! Thank you!! :)

8 0

4 years ago

12 - 3/4 (d + 16) = negative 5

Nutka1998 [239]

Answer: d=20/3

Step By Step:

Step 1, Simplify:

12-3/4(d+16)=-5

(-3/4)d+(12-12)=-5

(-3/4)d=-5

Step 2, Multiply each side by 4/(-3)

(4/-3)*(-3/4)d=(4/-3)*-5

d=20/3

8 0

3 years ago

Read 2 more answers

The equation of line WX is 2x + y = -5. What is the equation of a line perpendicular to line WX in slope-intercept form that con

sveticcg [70]

Answer:

The third choice is the one you want

Step-by-step explanation:

If we are to write the equation of a line perpendicular to WX, we first must determine what the slope of the WX is, because the line perpendicular to WX has a slope that is the flip of the slope of WX with the opposite sign. Solving for y takes care of finding the slope of WX:

2x + y = -5 so

y = -2x - 5

The slope is -2. That means that the reciprocal slope is 1/2. Using that slope along with the coordinates x = -1 and y = -2, we first write the line using point-slope form and then solve it for y. Start by filling in the m, the x value and the y value:

$y - (-2) = \frac{1}{2}(x-(-1))$

Getting rid of the double negatives gives us:

$y+2=\frac{1}{2}(x+1)$

Distributing then gives us:

$y+2=\frac{1}{2}x+\frac{1}{2}$

And finally solving for y (I am going to express the 2 on the left as 4/2 when I move it by subtraction in order to add those fractions):

$y=\frac{1}{2}x+\frac{1}{2}-\frac{4}{2}$

And the final equation in slope-intercept form is:

$y=\frac{1}{2}x-\frac{3}{2}$

8 0

3 years ago

Find the solution of this system of equations. Separate the x- and the y- values with a comma. X=6+y -8x+9y=-29

WINSTONCH [101]

Answer:

x= 25, y = 19

Step-by-step explanation:

Solve the following system:

{x = y + 6 | (equation 1)

9 y - 8 x = -29 | (equation 2)

Express the system in standard form:

{x - y = 6 | (equation 1)

-(8 x) + 9 y = -29 | (equation 2)

Swap equation 1 with equation 2:

{-(8 x) + 9 y = -29 | (equation 1)

x - y = 6 | (equation 2)

Add 1/8 × (equation 1) to equation 2:

{-(8 x) + 9 y = -29 | (equation 1)

0 x+y/8 = 19/8 | (equation 2)

Multiply equation 2 by 8:

{-(8 x) + 9 y = -29 | (equation 1)

0 x+y = 19 | (equation 2)

Subtract 9 × (equation 2) from equation 1:

{-(8 x)+0 y = -200 | (equation 1)

0 x+y = 19 | (equation 2)

Divide equation 1 by -8:

{x+0 y = 25 | (equation 1)

0 x+y = 19 | (equation 2)

Collect results:

Answer: {x = 25 , y = 19

6 0

3 years ago

Read 2 more answers

Prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1​

Prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1