number properties, 3 edition ,chapter 10 ,#14, page 180

[sowjanyaangara]

14) X= positive ,odd integer
QUANTITY A (-3)^x

QUANTITY B -2^2x


for -2^2x, any odd number multiplied by even number will make it even number.so 2x should be even number. when negative value multiplied even number of times make the number positive, making option B is greater. but explanation in the book is like this
-2^2x= -(2^2)^x= -4^x. In which situation minus sign is applied after multiplication?. Please explain

[tommywallach]

Hey Sowjan,

This is a typical issue that confuses people. If the negative symbol is not included in a parenthetical, it will always be applied after the exponent.

(-2)^2 = 4

-2^2 = -4

For example, if x = 1:

Quantity A: (-3)^1 = -3

Quantity B: -2^2 = -4

As you can see, this is the same as -4^1, because:

-2^2x = -(2^2)^x = -4^x

Hope that helps!

-t

P.S. This error is listed in the "common exponent errors" table at the end of the exponents chapter.