Question

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

Answer 1

Answer:

1. The correct option is d.

2. The correct option is c.

3. The correct option is a.

Step-by-step explanation:

1.

The given expression is

$3a^4b^{-2}c^3$

Using property of exponent the given expression can be written as

$\frac{3a^4c^3}{b^{2}}$               $[\because a^{-n}=\frac{1}{a^n}]$

Therefore, the correct option is d.

2.

The given expression is

$-a^{-2}$

Using property of exponent the given expression can be written as

$-\frac{1}{a^{2}}$               $[\because a^{-n}=\frac{1}{a^n}]$

Put a=-5

$-\frac{1}{(-5)^{2}}$

$-\frac{1}{25}$

Therefore option c is correct.

3.

The given expression is

$(-m)^{-3}n$

Using property of exponent the given expression can be written as

$\frac{n}{(-m)^3}$

Put m=2 and n=-24.

$\frac{-24}{(-2)^3}$

$\frac{-24}{-8}$

$\frac{24}{8}=3$

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