Question

Simplify. Assume no variable is 0.

#16-23 please

85 points!!!!! This is the jumbo pack!!!!

Answer 1

Q16

First, we multiply the variable x together:

and remove brackets:

Now, we multiply the variable y:

Hence:

Use the rule

Thus,

Multiply:

Q17

Multiply the variable b together:

Multiply the variable c together:

Multiply.

Q18:

Divide the numerator and denominator by a:

Apply the rule that

Hence, the equation will be

which is finally

Q19:

Do the same rule said above:

Do the rule again:

Q20:

Cancel the common factor of 7:

Thus,

Cancel common factor of y^5

Q21:

Cancel the common factor which is 9:

"Move" the variable a up using the rule:

"Move" the variable b down using the rule:

"Move" the variable c up using the rule

Q22:

Use the rule:

Hence,

Q23:

Using the same rule above,

Therefore,

you get your answer.

Answer 2

Explanation:

Q16

`( {5x}^(3) {y}^( - 5) )( {4xy}^(3) )`

First, we multiply the variable x together:

`{x}^(3) * x = {x}^(4)`

and remove brackets:

`{5y}^( - 5) * {4x}^(4) * {y}^(3)`

Now, we multiply the variable y:

`{y}^( - 5) * {y}^(3) = {y}^( - 2)`

Hence:

`5 * 4 {x}^(4) * {y}^( - 2)`

Use the rule

`{x}^( - y) = \frac{1}{ {x}^(y) }`

Thus,

`5 * 4 {x}^(4) * \frac{1}{ {y}^(2) }`

Multiply:

`\frac{20 {x}^(4) }{ {y}^(2) }`

Q17

`( - 2 {b}^(3) c)(4 {b}^(2) {c}^(2) )`

`- 2 {b}^(3) c* 4 {b}^(2) {c}^(2)`

Multiply the variable b together:

`- 2c * 4 {b}^(5) {c}^(2)`

Multiply the variable c together:

`- 2 * 4 {b}^(5) {c}^(3)`

Multiply.

`- 8 {b}^(5) {c}^(3)`

Q18:

`\frac{ {a}^(3) {n}^(7) }{a {n}^(4) }`

Divide the numerator and denominator by a:

`\frac{ {a}^(2) {n}^(7) }{ {n}^(4) }`

Apply the rule that

`\frac{ {x}^(y) }{ {x}^(z) } = {x}^(y - z)`

Hence, the equation will be

`{a}^(2) {n}^(7 - 4)`

which is finally

`{a}^(2) {n}^(3)`

Q19:

`\frac{ - {y}^(3) {z}^(5) }{ {y}^(2) {z}^(3) }`

Do the same rule said above:

`- \frac{ {z}^(5) {y}^(3 - 2) }{ {z}^(3) }`

`- \frac{y {z}^(5) }{ {z}^(3) }`

Do the rule again:

`- y {z}^(5 - 3)`

`- y {z}^(2)`

Q20:

`\frac{ - 7 {x}^(5) {y}^(5) {z}^(4) }{21 {x}^(7) {y}^(5) {z}^(2) }`

Cancel the common factor of 7:

`- \frac{ {x}^(5) {y}^(5) {z}^(4) }{3 {x}^(7) {y}^(5) {z}^(2) }`

`- \frac{ {y}^(5) {z}^(4) }{3 {y}^(5) {z}^(2) {x}^(7 - 5) }`

Thus,

`- \frac{ {y}^(5) {z}^(4) }{3 {y}^(5) {z}^(2) {x}^(2) }`

Cancel common factor of y^5

`- \frac{ {z}^(4) }{3 {z}^(2) {x}^(2) }`

`- \frac{ {z}^(4 - 2) }{3 {x}^(2) }`

`- \frac{ {z}^(2) }{3 {x}^(2) }`

Q21:

`\frac{9 {a}^(7) {b}^(5) {c}^(5) }{18 {a}^(5) {b}^(9) {c}^(3) }`

Cancel the common factor which is 9:

`\frac{{a}^(7) {b}^(5) {c}^(5) }{2 {a}^(5) {b}^(9) {c}^(3) }`

"Move" the variable a up using the rule:

`\frac{{a}^(7 - 5) {b}^(5) {c}^(5) }{2 {b}^(9) {c}^(3) }`

`\frac{{a}^(2) {b}^(5) {c}^(5) }{2 {b}^(9) {c}^(3) }`

"Move" the variable b down using the rule:

`\frac{{a}^(2) {c}^(5) }{2 {c}^(3) {b}^(9 - 5) }`

`\frac{{a}^(2) {c}^(5) }{2 {c}^(3) {b}^(4) }`

"Move" the variable c up using the rule

`\frac{{a}^(2) {c}^(5 - 3) }{2 {b}^(4) }`

`\frac{{a}^(2) {c}^(2) }{2 {b}^(4) }`

Q22:

`( {n}^(5) {)}^(4)`

Use the rule:

`({x}^(y) {)}^(z) = {x}^(yz)`

Hence,

`{n}^(5 * 4)`

`{n}^(20)`

Q23:

`( {z}^(3) {)}^(6)`

Using the same rule above,

`{z}^(3 * 6)`

Therefore,

`{z}^(18)`