Which expression has the greatest value?
$(15-1)^0$
$(1+2)^3$
$(2 \times 4)^1$
$(5-2)^2$
Answer (1)
Evaluate each expression:
( 15 − 1 ) 0 = 1
( 1 + 2 ) 3 = 27
( 2 × 4 ) 1 = 8
( 5 − 2 ) 2 = 9
Compare the values: 1, 27, 8, 9.
Identify the greatest value: 27.
The expression with the greatest value is: ( 1 + 2 ) 3
Explanation
Understanding the Problem We are given four expressions and we need to find out which one has the greatest value. The expressions are: ( 15 − 1 ) 0 , ( 1 + 2 ) 3 , ( 2 × 4 ) 1 , and ( 5 − 2 ) 2 .
Evaluating the Expressions Let's evaluate each expression:
( 15 − 1 ) 0 = ( 14 ) 0 = 1 . Any non-zero number raised to the power of 0 is 1.
( 1 + 2 ) 3 = ( 3 ) 3 = 3 × 3 × 3 = 27 .
( 2 × 4 ) 1 = ( 8 ) 1 = 8 . Any number raised to the power of 1 is the number itself.
( 5 − 2 ) 2 = ( 3 ) 2 = 3 × 3 = 9 .
Comparing the Values Now we compare the values we obtained: 1, 27, 8, and 9. The greatest value among these is 27. Therefore, the expression with the greatest value is ( 1 + 2 ) 3 .
Examples
Exponents are used to calculate compound interest. For example, if you invest money in a bank account that pays compound interest, the amount of money you have at the end of each year can be calculated using an exponent. Understanding exponents helps you calculate how quickly your investments will grow. Also, exponents are used in computer science to calculate memory and storage capacity.
