17 Questions
In the expression $4^2$, which part represents the exponent?
$2$
Following the PEMDAS rule, what should be solved first in the expression $3 + 4 * 2^2$?
$4 * 2^2$
What is the result of $2^3 * 6^2$?
$432$
According to the order of operations, which operation should be done first in $5^2 - 3 * 2$?
Exponentiation
If given the expression $7^2 / 49$, what is the correct simplified form?
$1$
In the calculation $6 * 3^2 / 2$, which operation should be conducted first according to the order of operations?
$3^2 / 2$
In the expression $5 \times 4 + 3$, which operation is performed first?
Multiplication
What is the result of the expression $9 \div 3 - 2$?
1
Which operation has higher precedence in the expression $2^3 \times 6^2$?
Exponentiation
In the expression $4^2 \div 49$, which part represents the exponent?
2
Which operation should be conducted first in the calculation $6 \times 3^2 \div 2$?
Exponentiation
In the expression $5^2 - 3 \times 2$, which operation should be done first?
Exponentiation
What is the result of the expression $3 * (4 + 2)$?
$18
In the expression $(8 - 2) \div 3$, what is the final result?
$2
Evaluate the expression: $5 + 3 * (2 + 1)$
$17
What is the result of $(10 \div 2) + 3 * 2$?
$11
Simplify the expression: $(6 * 2) + (4 \div 2)$
$14
Study Notes
Order of Operations and Exponents
The order of operations, often referred to as PEMDAS (or BODMAS outside the US), is a set of rules designed to ensure consistency when solving mathematical expressions. It provides a universal guideline for following a specific sequence of steps to resolve complex calculations accurately. One of the main components of this order is the handling of exponents.
Exponents in Mathematics
An exponent is represented by a small superscript number, which indicates the power to which the base number is raised. For example, in the expression 2^3, the base number is 2, and the exponent is 3, meaning 2 is raised to the power of 3.
Exponents and the Order of Operations
Exponents play a crucial role in the order of operations because they involve multiplying or dividing the value of a given number repeatedly. According to the PEMDAS rule, after parentheses, you must address any exponents before proceeding with other operations. This ensures that you don't accidentally overwrite the result obtained through exponentiation.
Let's consider an example:
5 * 3^2
According to the PEMDAS rule, we must handle the exponent before the multiplication:
5 * 3^2 -> 5 * 9
So, the correct calculation would be:
5 * 9 = 45
If we had followed a different order, we might get a different answer, highlighting why the order of operations is so important.
Test your knowledge on the order of operations and exponents in mathematics with this quiz. Understand the rules of PEMDAS and how to correctly handle exponents in mathematical expressions to ensure accurate calculations.
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