Question

learn evaluating numerical expressions
an expression of the form a^n is read “a to the nth power”. the word
power is used to refer to the exponent. the value of the exponential of
the expression.
when n is a positive integer, the exponent indicates the number of
times a number is multiplied by itself. in a power, the base is the
number being multiplied by itself.
to evaluate an expression means to find its value. if a numerical
expression contains more than one operation, then the key is to know
which operation to perform first. this is called the order of
operations.
key concept - order of operations
step 1 evaluate expressions inside grouping symbols.
step 2 evaluate all powers.
step 3 multiply and/or divide from left to right.
step 4 add and/or subtract from left to right.
example 4 evaluate expressions
evaluate each expression.
a. 2^4
2^4 = 2·2·2·2
use 2 as a factor 4 times.
multiply.
b. 4^5
4^5 = 4·4·4·4·4
use 4 as a factor 5 times.
multiply.
example 5 order of operations
evaluate 20 - 7 + 8^2 - 7·11.
20 - 7 + 8^2 - 7·11 = 20 - 7 + 64 - 7·11
= 20 - 7 + 64 - 77
multiply 7 and 11.
= 13 + 64 - 77
= 77 - 77
= 0
subtract 77 from 77.

Explanation:

Step1: Evaluate powers

$2^4=2\times2\times2\times2 = 16$

Step2: Evaluate powers

$4^5=4\times4\times4\times4\times4=1024$

Step3: Evaluate expression with multiple - operations

$20 - 7+8^2 - 7\times11=20 - 7 + 64-77$ (Evaluate power $8^2 = 64$ and multiply $7\times11 = 77$)
$=(20 - 7)+64 - 77=13 + 64-77$ (Subtract $20 - 7 = 13$)
$=(13 + 64)-77=77 - 77$ (Add $13+64 = 77$)
$=0$ (Subtract $77 - 77$)

Answer:

a. $16$
b. $1024$
c. $0$