Question

What is the simplified form of 3a^4b^-2c^3?

a. (81a^4c^3)/(b^2)
b. (81a^4)/(b^2c^3)
c. (3a^4)/(b^2c^3)
d. (3a^4c^3)/(b^2) D What is -a^-2 if a = -5?
a. -25
b. 25
c. -1/25
d. 1/25 D What is (-m)^-3n if m = 2 and n = -24?
a. 3
b. -3
c. 4
d. -4 A

Answer 1

1. The correct option is d.

2. The correct option is c.

3. The correct option is a.

Explanation:

1.

The given expression is

`3a^4b^(-2)c^3`

Using property of exponent the given expression can be written as

`(3a^4c^3)/(b^(2))`
`[\because a^(-n)=(1)/(a^n)]`

Therefore, the correct option is d.

2.

The given expression is

`-a^(-2)`

Using property of exponent the given expression can be written as

`-(1)/(a^(2))`
`[\because a^(-n)=(1)/(a^n)]`

Put a=-5

`-(1)/((-5)^(2))`

`-(1)/(25)`

Therefore option c is correct.

3.

The given expression is

`(-m)^(-3)n`

Using property of exponent the given expression can be written as

`(n)/((-m)^3)`

Put m=2 and n=-24.

`(-24)/((-2)^3)`

`(-24)/(-8)`

`(24)/(8)=3`

Therefore option a is correct.

Answer 2

1. Simplified form of: 3 a^4 * 4 b^(-2) * c^3 =
= ( 3 a^4 * 4 c^3 ) / ( b^2 )
Answer: d.
2. If a = - 5,
- a^(-2) = - ( - 5 )^(-2) = - ( 1/ 5^2 ) = - 1/25
Answer: c.
3. If m = 2 and n = - 24:
( - 2 )^(-3) * ( - 24 ) = 1 / (- 2 )^3 * ( - 24 ) = - 1 / 8 * ( - 24 ) = 24 / 8 = 3
Answer: a. 3