Below are two sets of pairs of exponential expressions.

Question

i need to simplify and determine if the pairs are equivalent then exp if the parenthesis are necessary in each of the exponential expressions.

 

-4² and (-4)²

-2³ and (-2)³

Answer 1

By PEMDAS, exponents are evaluated before multiplication (or addition).

-4²: the 4 is squared before the minus sign (which means "multiply by -1") is applied. So it's -16.

(-4)²: The (-4) is squared, so it's (-4)(-4) = 16

This is exactly the same as what Arturo said, just explained a little differently.

Answer 2

Carolyn,

 

-4² = -16 while (-4)² = 16 

 

-2³ = -8 and (-2)³ = -8

 

Note that the parenthesis is necessary in the first pair but not for the second pair.

 

It matters whether the exponent is an even number or an odd number when the base is a negative number.

 

Negative numbers raised to even exponents produce positive results while negative numbers raised to odd exponents produce negative results.

 

Also, when parentheses are not used, they are implied.

 

So, -4² = -(4)² = -(16) = -16 and -2³ = -(2)³ = -(8) = -8

 

(-4)² = (16) = 16 while (-2)³ = (-8) = -8

 

I hope this helps.

 

 

Answer 3

-4² = -(4²) = -16 

(-4)² = (-1)²(4)² = (1)(16) = 16

These are not equivalent.

 

-2³ = -(2³) = -8

(-2)³ = (-1)³(2)³ = (-1)(8) = -8

These are equivalent.