An exponent is a number that represents the number of times a base number is multiplied by itself. In evaluating an expression with exponents, the exponent tells us how many times the base number should be multiplied by itself. For example, in the expression 2^3, the exponent 3 indicates that the base number 2 should be multiplied by itself 3 times, resulting in 8.
To simplify an expression with exponents, you can use the rules of exponents. For example, when multiplying two numbers with the same base, you can add the exponents. So, 2^3 * 2^4 can be simplified to 2^(3+4) which is equal to 2^7. You can also use the rule for dividing two numbers with the same base, where you subtract the exponents. For example, (2^5)/(2^2) can be simplified to 2^(5-2) which is equal to 2^3.
The order of operations for evaluating expressions with exponents is the same as any other expression: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). This means that exponents should be evaluated before any other operations in an expression.
Yes, negative exponents are allowed in expressions. A negative exponent indicates that the base number should be divided by itself the number of times indicated by the exponent. For example, 2^-3 is equal to 1/(2^3) which is equal to 1/8. Negative exponents can also be written as positive exponents in the denominator, so 2^-3 is equivalent to 1/(2^3) which can be written as 2^3 in the denominator.
A zero exponent indicates that the base number should be multiplied by itself zero times, which is equal to 1. So, any expression with a zero exponent will result in a value of 1. For example, 5^0 is equal to 1, as is 2^0 or 100^0. It is important to note that this rule only applies when the base number is not 0. If the base number is 0, then the expression is undefined.