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PtrTon · Answer 1 · 2019-08-25T21:53:58+0000

ANSWER TO QUESTION 1

$(3 {n}^(4) + 1) + ( - 8 {n}^(4) + 3) - ( - 8 {n}^(4) + 2)$

Let us expand the parenthesis first.

$(3 {n}^(4) + 1) + ( - 8 {n}^(4) + 3) - ( - 8 {n}^(4) + 2) = 3 {n}^(4) + 1 + - 8 {n}^(4) + 3 + 8 {n}^(4) - 2$

This will simplify to,

$(3 {n}^(4) + 1) + ( - 8 {n}^(4) + 3) - ( - 8 {n}^(4) + 2) = 3 {n}^(4) + 2$

ANSWER TO QUESTION 2

We want to write

6.5 * 10 - 7

in standard notation.

Let us simplify first to obtain,

6.5 * 10 - 7 = 65 - 7

In standard notation we have,

$6.5 * 10 - 7 = 5.8 * {10}^(1)$

ANSWER TO QUESTION 3

This question requires us to write
(m-n)(m+n)

in words.

Subtract

from

and multiply the result by the sum of

and

.

ANSWER TO QUESTION 4

We want to simplify

$( - 3 {t}^(2) {u}^(3) )(5 {t}^(7) {u}^(8) ).$

We use the laws of exponents to simplify the above expression.

$( - 3 {t}^(2) {u}^(3) )(5 {t}^(7) {u}^(8) ) = - 3 * 5 * {t}^(2) * {t}^(7) * {u}^(3) * {u}^(8)$

Recall that,

${a}^(m) * {a}^(n) = {a}^(m + n)$

This implies that,

$( - 3 {t}^(2) {u}^(3) )(5 {t}^(7) {u}^(8) ) = - 15 * {t}^(2 + 7) * {u}^(3 + 8)$

This simplifies to,

$( - 3 {t}^(2) {u}^(3) )(5 {t}^(7) {u}^(8) ) = - 15 * {t}^(9) * {u}^(11)$

ANSWER TO QUESTION 5.

We want to complete the property of exponents given by,

${b}^(n) * {b}^(m)$

According to this product property of exponents,since the bases are the same we write down one base and add the exponents to obtain,

${b}^(n) * {b}^(m) = {b}^(m + n)$

ANSWER TO QUESTION 6.

Please see attachment for the long division

ANSWER TO QUESTION 7.

We were given the expression,

m(y) = (2y + 5)/(y - 7)