Question

1.What is the simplified form of each expression?

7x^–8 × 6x^3

a. 42/x^5
b. 1/42x^5
c. 42x^11
d. 13x^–5

(–2x8) · 3y9 · 2x4

a. 3x^12y^9
b. –12x^72y^9
c. –12xy^21
d. –12x^y^9

2. Find the simplified form of the expression. Give your answer in scientific notation.

(8 x 10^7) (7 x 10^4)

a. 1.5 × 10^12
b. 5.6 × 10^12
c. 1.5 x 10^29
d. 5.6 x 10^29


(7 × 10^–4)(9 × 10^–10)

a. 6.3 × 10^–13
b. 63 × 10^–13
c. 6.3 × 10^–15
d. 6.3 × 10^–16

Answer 1

Answer with explanation:

Ques 1)

A)

We are given a expression as:

`7x^(-8)* 6x^3`

It could also be written as:

`(7* 6)* x^(-8)* x^3\\\\\\=42* x^(-8+3)\\\\\\=42x^(-5)\\\\\\=(42)/(x^5)`

Option: a is the answer.

B)

`(-2x^8)* 3y^9* 2x^4`

which is solved as follows:

`(-2* 3* 2)* x^8* y^9* x^4\\\\\\=-12x^(8+4)* y^9\\\\\\=-12x^(12)y^9`

Ques 2)

A)

The expression is:

`(8* 10^7)(7* 10^4)`

It is solved as:

`=(8* 7)* 10^7* 10^4\\\\\\=56* 10^(7+4)\\\\\\=56* 10^(11)\\\\\\=5.6* 10^(12)`

Option: b is the answer.

B)

`(7* 10^(-4))(9* 10^(-10))`

On simplifying:

`=7* 9* 10^(-4)* 10^(-10)\\\\\\=63* 10^(-4-10)\\\\\\=63* 10^(-14)\\\\\\=6.3* 10^(-14+1)\\\\\\=6.3* 10^(-13)`

Option: a is the answer.