Problem 55 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 4^{3}+10 \div 2 \cdot 6 $$

Step-by-Step Solution

Answer

94

Step 1 - Evaluate the exponent

Begin by evaluating the exponent in the expression. Calculate \[ 4^3 \]which is \[ 4 \times 4 \times 4 = 64 \]So, the expression becomes:\[ 64 + 10 \/ 2 \cdot 6 \]

Step 2 - Perform the division

Next, perform the division operation. Divide \[ 10 \div 2 \]which equals \[ 5 \]So, the expression becomes:\[ 64 + 5 \cdot 6 \]

Step 3 - Perform the multiplication

Now, perform the multiplication operation.\[ 5 \cdot 6 \]which equals \[ 30 \]So, the expression becomes:\[ 64 + 30 \]

Step 4 - Perform the addition

Finally, perform the addition to get the result.\[ 64 + 30 = 94 \]

Key Concepts

Exponentiation

Exponentiation is the process of raising a number to a power. It means multiplying the base number by itself a specified number of times. For example, in the expression \( 4^3 \), 4 is the base and 3 is the exponent. This means we have to multiply 4 by itself three times: \ 4 \times 4 \times 4 = 64. Exponentiation is always performed first in expressions unless there are parentheses that change the order.

Division

Division is one of the basic arithmetic operations and is essentially the opposite of multiplication. In the expression \( 10 \div 2 \), we divide 10 by 2, which equals 5. Division is performed after exponentiation but before addition and subtraction unless there are parentheses that modify this order.

Multiplication

Multiplication, another fundamental arithmetic operation, involves adding a number to itself a certain number of times. For instance, \( 5 \cdot 6 \) means adding 5 six times (or 6 five times): \( 5 + 5 + 5 + 5 + 5 + 5 = 30 \). In the order of operations, multiplication is performed after division but before addition and subtraction unless specified otherwise by parentheses.

Addition

Addition is the process of finding the total or sum by combining two or more numbers. In the given expression, the last step is to add 64 and 30: \( 64 + 30 = 94 \). Addition is performed last in the order of operations, after all other operations (exponentiation, division, multiplication) have been completed, unless modified by parentheses.