Table of Contents
- 1 What has the same variables raised to the same exponents?
- 2 Do like terms have the same variable and the same exponent?
- 3 What do you do when two numbers have the same exponent?
- 4 When an exponent is raised to another exponent?
- 5 What’s the difference between three factors with exponents?
- 6 When to multiply the exponent to the outer exponent?
- 7 How to make a negative exponent a positive exponent?
What has the same variables raised to the same exponents?
Like terms are terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only like terms can be combined. We combine like terms to shorten and simplify algebraic expressions, so we can work with them more easily.
Do like terms have the same variable and the same exponent?
Like terms are variables that have the same letter and same exponent. We combine them by adding or subtracting the coefficients (the number in front of the letter). The exponents will stay the same after adding or subtracting like terms.
What does it mean when a variable has an exponent?
What is a Variable with an Exponent? A Variable is a symbol for a number we don’t know yet. An exponent (such as the 2 in x2) says how many times to use the variable in a multiplication.
What do you do when two numbers have the same exponent?
When you multiply two numbers or variables with the same base, you simply add the exponents. When you multiply expressions with the same exponent but different bases, you multiply the bases and use the same exponent.
When an exponent is raised to another exponent?
When an exponent is being raised by another exponent, we just multiply the powers of the exponents and keep the base the same.
Can you add variables with different exponents?
In order to add or subtract variables with exponents, you need to have like bases and like exponents, which means that the bases and exponents are the same. Even though the exponents are the same, these cannot be added or subtracted because their bases or exponents are different.
What’s the difference between three factors with exponents?
The only difference is that there are three (3) factors with exponents. We just need to distribute the outer exponent to each of the inner exponents. When a quotient is raised to a power, copy the factor on the numerator then multiply its exponent to the outer exponent.
When to multiply the exponent to the outer exponent?
When a quotient is raised to a power, copy the factor on the numerator then multiply its exponent to the outer exponent. We must do the same with the factor in the denominator where we copy it then multiply its exponent to the outer exponent. Here, we also need to assume that m m is an integer. Simplify the exponential expression.
How to divide exponential expressions with the same base?
When dividing exponential expressions with the same base where the base is a nonzero real number, copy the common base then subtract the top exponent by the bottom exponent. We must suppose here that n n belong to the set of integers. Simplify the quotient of exponential expressions. The fractional bar implies that we are going to divide.
How to make a negative exponent a positive exponent?
1 1. Make sure to reduce the fraction to its lowest term. Any nonzero number raised to a negative exponent is not in standard form. We will need to do some rearranging. Move the base with a negative exponent to the opposite side of the fraction, then make the exponent positive. The assumptions here are n n is an integer. {2^ { – \\,4}} 2−4.