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2 years ago

Simplify each expression. The simplified expression should have no exponents. (40 points)

Mathematics

1 answer:

Elina [12.6K]2 years ago

4 0

Answer:

Step-by-step explanation:

Cancel the common factor of 4y

-3x/7x^4 . (21x^5y^2)

Cancel the common factor of 7x^4

-3x .(3xy^2)

Multiply 3 by -3

-9x . (xy^2)

Raise x to the power of 1

-9(x^1x).y^2

Raise x to the power of 1

-9(x^1x^1) . y^2

Use the power rule a^m a^n = a^m+n to combine exponents

-9x^1+1 .y^2

-9x^2y^2, Thus final answer is -9x^2y^2

10.

Cancel the common factor of 3

-x^5/x^13 . 2x^10y/5y^2

cancel the common factor of x^10

-x^5/x^3 . 2y/5y^2

Multiply -x^5/x^3 by 2y/5y^2

Multiply 2 by -1

-x^5(2y)/x^3(5y^2)

Cancel the common factor of x^5 and x^3

-2x^2y/5y^2

Cancel the common factor of y and y^2

-2x^2/5y

Thus final answer = -2x^2/5y

11.

Cancel the common factor of 4x

y^11/x^7y^6 . 6x^8y/2x^2

Cancel the common factor of x^7y

y^11/y^5 . 6x/2x^2

Multiply y^11/y^5 and 6x/2x^2

y^11 (6x)/y^5 (2x^2)

Cancel the common factor of y^11 and y^5

y^6 (6x)/2x^2

Cancel the common factor of 6 and 2

y^6 (3x)/x^2

Cancel the common factor of x and x^2

y^6 . (3)/x

Move 3 to the left of y^6

3y^6/x Thus final answer = 3y^6/x

12.

Cancel the common factor of y^6

y^4/2x^3 . 20x^14/x

Cancel the common factor of 2x^3

y^4 . 10x^11/x

combine y^4 and 10x^11/x

y^4 (10x^11)/x

cancel the common factor of x^11 and x

y^4 (10x^10)

Rewrite using the commutative property of multiplication

10y^4 x^10, Thus final answer = 10y^4 x^10

13.

Combine

5x^-2 (2y^3)/3x . x^10

Multiply x by x^10 by adding the exponents(negative exponent rule

5x^-2 (2y^3)/3x^11 x2

Multiply x^11 by x^2 by adding exponents

5(2y^3)/3x^13

Multiply 5 by 2

10y^3/3x^13 thus final answer = 10y^3/3x^13

14.

Move x^-1 to the numerator using the negative exponent rule

(5xyx/8y^2)^2 . 26y^3/5x^2y^5

Multiply x by x by adding the exponents

(5x^2y/8y^2)^2 . 26y^3/5x^2y^5

Cancel the common factor of y and y^2

(5x^2/8y)^2 . 26y^3/5x^2y^5

Use the power rule (ab)^n = a^n b^n to distribute the exponent

5^2(x^2)^2/8^2y^2 . 26y^3/5x^2y^5

Simplify the numerator

25x^4/8^2y^2 . 26y^3/5x^2y^5

Simplify terms

65x^2/32y^4 Thus final answer is 65x^2/32y^4

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Use the distributive property to expand the following expression (9m-6)7 please help

Drupady [299]

Answer:2/3

Step-by-step explanation:

Simplifying

(9m + -6) * 7 = 0

Reorder the terms:

(-6 + 9m) * 7 = 0

Reorder the terms for easier multiplication:

7(-6 + 9m) = 0

(-6 * 7 + 9m * 7) = 0

(-42 + 63m) = 0

Solving

-42 + 63m = 0

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '42' to each side of the equation.

-42 + 42 + 63m = 0 + 42

Combine like terms: -42 + 42 = 0

0 + 63m = 0 + 42

63m = 0 + 42

Combine like terms: 0 + 42 = 42

63m = 42

Divide each side by '63'.

m = 0.6666666667

Simplifying

m = 0.6666666667=2/3 when simplified

7 0

2 years ago

Read 2 more answers

PLEASE HELP ME I DON T UNDERSTAND IF YOU PLEASE COULD HELP ME I WOULD GREATLY APPRECIATE IT REALLY THANK YOU

butalik [34]

Find the length of one side.

V = s^3

s = cube root of V

V = 729

s = cube root 729

s = 9

Put this into your calculator as 729^0.333333333

It should bring back 9 or 8.999999 something which means 9.

Net

The net is shown below. You will have to do the labeling. But I can tell you what you should label each face as?

Area of one face = s^2

s = 9

Area of one face = 9*9

Area of one face = 81

So when you draw this, each face should be labeled with 81.

It should have it's units (ft^2) if your marker is picky.

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There are 6 sides.

1 side has an area of 81 ft^2

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3 years ago

Before conducting some experiments, a scientist mixes 1/2 gram of Substance A with 3/4 grams of Substance B. If the scientist us

Tju [1.3M]

Answer: 10

Step-by-step explanation:

$(\frac{1}{2}+\frac{3}{4})$ ÷ $\frac{1}{8}$

= $(\frac{1}{2}(\frac{2}{2})+\frac{3}{4})$ ÷ $\frac{1}{8}$

= $(\frac{2}{4}+\frac{3}{4})$ ÷ $\frac{1}{8}$

= $(\frac{5}{4})$ ÷ $\frac{1}{8}$

= $(\frac{5}{4})$ x $\frac{8}{1}$

= $\frac{40}{4}$

= 10

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3 years ago

I NEED URGENT ASSISTANCE

Nata [24]

Answer:

8 C sometimes

9 64x^8 y^11

10 c 1.28r^2/ t^9

Step-by-step explanation:

Algebraic Operations

Some basic rules must be fresh in our minds when trying to simplify complex algebraic expressions. For example, the power rule respect to the product or quotient:

$\displaystyle \left(\frac{x^n.y^m}{z^p}\right)^q= \frac{x^{qn}.y^{qm}}{z^{qp}}$

$\displaystyle \frac{x^n.x^q}{x^p}= x^{n+q-p}$

$\displaystyle x^{-n}=\frac{1}{x^n}$

Let's face the questions at hand

8. A number is raised to a negative exponent is negative?

Following the expressions recalled above, let's pick the expression

$\displaystyle 3^{-2}=\frac{1}{3^2}=\frac{1}{9}$

This is a negative power resulting in a positive number

Now we pick

$\displaystyle (-2)^{-3}=\frac{1}{(-2)^3}=-\frac{1}{8}$

This time, the negative power leads to a negative result, so it doesn't matter the sign of exponent to determine the sign of the result

Answer: C sometimes

9 simplify(4xy^2)^3(xy)^5

$(4xy^2)^3(xy)^5=4^3x^3(y^2)^3x^5y^5$

$=64x^3y^6x^5y^5$

$=64x^8y^{11}$

10 simplify(2t^-3)^3(0.4r)^2

$(2t^{-3})^3(0.4r)^2=2^3(t^{-3})^30.4^2r^2$

$=8t^{-9} 0.16 r^2$

$=1.28t^{-9} r^2$

$\displaystyle \frac{1.28 r^2}{t^9}$

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3 years ago

A salsa recipe uses 14 ounces of peppers and 7 ounces of onions

mixer [17]

Answer:

$s = salsa$

$p = peppers$

$o = onions$

$s = 14p + 7o$

Step-by-step explanation:

Hope this helps!

14 + 7 = 21 ounces.

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3 years ago