How do you evaluate #2\cdot 5^ { 3} + 0\cdot 5^ { 2} + 1\cdot 5^ { 1} + 4\cdot 5^ { 0}#?

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Answer 1 · 2017-11-23T06:32:13

Use Order of Operations

Using PEMDAS (or something like BODMAS, depending on where you live), you can break this down.

Parentheses/Brackets: We don't have any of these in the expression.

Exponents/Orders: #5^3 = 125#
#5^2 = 25#
#5^1 = 5# (Any #value^1# equals that #value * 1#)
#5^0 = 1# (Any #value^0# except for 0 equals 1)

#2 * 125 + 0 * 25 + 1 * 5 + 4 * 1#

Multiplication/Division: #2 * 125 = 250#
#0 * 25 = 0# (Any #value * 0# equals #0#)
#1*5 = 5#
#4 * 1 = 4#

#250 + 0 + 5 + 4#

Addition/Subtraction: #250 + 0 = 250#
#250 + 5 = 255#
#255 + 4 = 259#

#2\cdot 5^ { 3} + 0\cdot 5^ { 2} + 1\cdot 5^ { 1} + 4\cdot 5^ { 0} = 259#