Question

98 POINTS!!! Simplify the following expression.

(3x^4y^5z^5)^4 (2x^4y^-3z^-1)

Answer 1

Answer:

Hey mate...

here is your answer:-

Step-by-step explanation:

Move

$y^{ - 4}$

to the denominator using the negative exponent rule

$b^{ - n} 1 \div b^{n}$

=>

$2x ^{4} z ^{ - 3} \div 3x^{2} {y}^{ - 3} {z}^{4} {y}^{4}$

Simplify the denominator

Multiply

${y}^{ - 3}$

by

${y}^{7}$

by adding the exponents

$2 {x}^{4} \div 3 {x}^{2} y^{1} {z}^{4} {z}^{3}$

Simplify

$3 {x}^{2} {y}^{1} {z}^{4}$

$2 {x}^{4} \div 3 {x}^{2} y {z}^{4} {z}^{3}$

Multiply

${z}^{4}$

by

${z}^{3}$

by adding the exponent

Move

${z}^{3}$

$2 {x}^{4} \div 3 {x}^{2} y \ {z}^{3} {z}^{4}$

Use the power rule

${a}^{m} {a}^{n} = {a}^{m + n}$

to combine exponents

$2 {x}^{4} \div 3 {x}^{2} yz^{3 + 4}$

Add 3 and 4

$2 {x}^{4} \div 3 {x}^{2} yz^{7}$

Reduce the expression by cancelling the common factors.

Ffactor

${x}^{2}$

out of

$2x ^{4}$

${x}^{2} 2 {x}^{2} \div 3 {x}^{2} yz ^{7}$

Cancel the common factor.

Factor

${x}^{2}$

out of

$3 {x}^{2} yz ^{7}$

${x}^{2} 2 {x}^{2} \div {x }^{2} 3yz ^{7}$

Cancel the common factor.

Factor

${x}^{2} 2 {x}^{2} \div {x}^{2} 3yz ^{7}$

Now ,

Rewrite the expression.

$2x^{2} \div 3yz^{7}$

Hope it helps you...!!

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Answer 2

Answer:

(eq. 1) 2x - y - z = 15

-y = 15 - 2x + z

y = -15 + 2x - z

2. Substitute what that letter equals for that letter in the

other two equations and simplify:

(eq. 2) 4x + 5y + 2z = 10

4x + 5(-15 + 2x - z) + 2z = 10

4x - 75 + 10x - 5z + 2z = 10

14x - 3z - 75 = 10

(eq. 4) 14x - 3z = 85

(3q. 3) -x - 4y + 3z = -20

-x - 4(-15 + 2x - z) +3z = -20

-x + 60 - 8x + 4z + 3z = -20

-9x + 7z + 60 = -20

(eq. 5) -9x + 7z = -80

Now we have only a system in 2 equations and 2 unknowns:

(eq. 4) 14x - 3z = 85

(eq. 5) -9x + 7z = -80

3. Solve either equation for either letter.

I'll pick the easier equation to solve for the easier letter.

(eq. 4) 14x - 3z = 85

-3z = 85 - 14x

z = -85/3 + (14/3)x

4. Substitute what that letter equals for that letter in the

other equation and simplify:

(eq. 5) -9x + 7z = -80

-9x + 7[-85/3 + (14/3)x] = -80

-9x - 595/3 + (98/3)x = -80

-27x - 595 + 98x = -240

71x - 595 = -240

71x = 355

x = 5

5. Substitute that in the other letter in one of the

other equations in two letters and solve for a

second letter:

I'll substitute x = 5 in eq. 5:

(eq. 5) -9x + 7z = -80

-9(5) + 7z = -80

-45 + 7z = -80

7z = =35

z = -5

6. Finally substitute the numbers for the two letters

you have in one of the original equations and solve

for the last remaining letter:

I'll pick eq. 3 to substitute x = 5 and z = -5 in

(3q. 3) -x - 4y + 3z = -20

-(5) - 4y + 3(-5) = -20

-5 - 4y - 15 = -20

-4y - 20 = -20

-4y = 0

y = 0