Answered

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
B25
C-1/25
D1/25 D What is (-m)^-3n if m = 2 and n = -24?
A3
B-3
C4
D-4 A

Verified Answer :

HomertheGenius
  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

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.