In the expression 3×2 + y − 5, which of the following choices is the exponent in the term 3×2?
The Correct Answer and Explanation is :
In the expression 3x² + y − 5, the exponent in the term 3x² is 2.
Explanation:
In algebra, an exponent refers to the number that indicates how many times the base (in this case, x) is multiplied by itself. The term 3x² consists of three parts:
- The coefficient: The number in front of the variable, which is 3.
- The variable: In this case, the letter x represents an unknown quantity.
- The exponent: The small number written as a superscript (² in this case) to the right of the variable, which tells you how many times the variable is multiplied by itself.
In 3x², the variable is x, and the exponent is 2. This means that x is multiplied by itself once (i.e., x * x), and the result is then multiplied by the coefficient (3 in this case). So the entire term represents 3 times x-squared.
More on Exponents:
Exponents play a significant role in algebra and are a key part of understanding the relationship between numbers and variables. When a variable has an exponent, it tells you how many times the base variable is repeated as a factor. For example, in x², the exponent 2 indicates that x is multiplied by itself once: x * x.
If there were no exponent written, it would be understood as 1 by default. For example, x is the same as x¹ because any number raised to the power of 1 is itself. Similarly, a term without a variable (such as -5) can be considered as -5x⁰, because any number raised to the power of 0 equals 1.
Thus, in 3x², the 2 is the exponent, and it plays a key role in determining the value of the term.