Definitions
In the expression [[$ 2^4 = 2 \cdot 2 \cdot 2 \cdot 2 = 16 $]], the number 2 is called the base number, the number 4 is called the exponent and the number 16 is called the value of the power. If brackets are not used, the exponent only affects the number directly below the exponent.
The base number is [[$2$]]. The answer is negative because there is an odd number (1) of negative factors in the product.
b) [[$ (-2)^4 = (-2) \cdot (-2) \cdot (-2) \cdot (-2) = 16 $]]
The base number is [$-2$]]. The answer is positive because there is an even number (4) of negatives factors in the product.
Example 1
Simplify the powers.
a) [[$ -2^4 = -2 \cdot 2 \cdot 2 \cdot 2 = -16 $]]The base number is [[$2$]]. The answer is negative because there is an odd number (1) of negative factors in the product.
b) [[$ (-2)^4 = (-2) \cdot (-2) \cdot (-2) \cdot (-2) = 16 $]]
The base number is [$-2$]]. The answer is positive because there is an even number (4) of negatives factors in the product.