40 points simplifying exponents and rules of exponents simplify the expressions below: 2 4 3 0 4 6 4 -3 2 3 2

ANSWER

a. 16

b. 1

c. 64

d. 64

EXPLANATION

We want to simplify the following exponential expressions

a.

This implies that

b. Any non-zero number exponent zero is 1.

This implies that,

c. The given exponentiial expression is,

The bases are the same so we add the exponents.

This simplifies to,

d. We want to simplify:

This is the same as

We add the exponents now to get:

B.

Step-by-step explanation:

If you simplify both sides and you have both sides in the form, , if the the number in front of the variable, is the same while the constant number, , is different then you will have no solutions.

If you have same and same , then you have infinitely many solutions.

If you have different then you have one solution.

Let's simplify both sides of A:

Distribute:

Combine like terms on left hand side:

The left hand side and right hand side have the same value no matter the x.  This has infinitely many solutions.

Let's simplify both sides of B:

Distribute:

Combine like terms on either side:

This is going to have no solutions.  If you thought about graphing y=4x+11 and y=4x+3 you would see that they are parallel and never cross.  

You could also try and solve it.

Subtract 4x on both sides:

11 is never 3.

11 isn't 3.

11=3 is not true which means there is no satisfying the equation labeled B.

Let's simplify both sides of C:

Distribute:

Combine like terms on either side:

This is going to have one solution.

We can solve it and see.

Subtract 4x on both sides:

Subtract 15 on both sides:

Divide both sides by 2:

0 is the one number that will make both sides the same for equation C.

Let's simplify both sides of D:

Distribute:

Combine like terms on left hand side:

These are the exact same expression on both sides and therefore will have the same value no matter the value of x you choose to plug in.

There are infinitely many solutions.