Sage-Tips

How do you compare exponents and powers?

Writing a number as an exponential expression makes it easy to compare to other numbers — the number with the higher exponent is the larger number. For example, compare two numbers: 943,260,000,000,000,000,000,000 and 8,720,000,000,000,000,000,000,000. Write them as numbers between 1 and 10, times a power of ten.

What do you do with exponents with different bases?

Multiplying exponents with different bases First, multiply the bases together. Then, add the exponent. Instead of adding the two exponents together, keep it the same.

How do you compare big numbers?

To compare two numbers, follow these steps:

1. Write the numbers in a place-value chart.
2. Compare the digits starting with the greatest place value.
3. If the digits are the same, compare the digits in the next place value to the right. Keep comparing digits with the same place value until you find digits that are different.

What do you do when you compare numbers?

When comparing numbers, we often use these symbols like > < and = . Comparing In general, if a and b are two numbers: a > indicates that number a is greater than number b; a < b shows that a is less than b, and lastly, a = b shows that number a is equivalent to number b.

How do you compare numbers that are expressed in different ways?

Comparing Numbers

=	When two values are equal, we use the “equals” sign	example: 2+2 = 4
<	When one value is smaller than another, we can use a “less than” sign.	example: 3 < 5
>	When one value is bigger than another, we can use a “greater than” sign	example: 9 > 6

How do you add exponents with the same base and different powers?

Remember, to add or subtract numbers that have exponents you must first make sure that the base and exponent of the two terms you are trying to add or subtract are the same. If they are the same, then all you have to do is add together their coefficients and keep the base and exponent the same.

How do we compare the numbers?

The easiest way to compare numbers is to draw a number line and mark the numbers you want to compare on it. On the number line, the value of the number is increasing from left to the right. The conclusion is that if the number is positioned to the right of the number , then the number is larger than the number .

How do we compare numbers what symbols do we use?

Checking which number is bigger or smaller is called comparing. We use comparison symbols (>, < and =) to compare numbers. TIP FOR REMEMBERING! For greater than and less than symbols, the wide open mouth of the symbol always faces the larger number.

How do we compare numbers?

How do you find the exponents of two numbers with different bases?

When the bases are different and the exponents of a and b are the same, we can divide a and b first: a n / b n = (a / b) n. Example: 6 3 / 2 3 = (6/2) 3 = 3 3 = 3⋅3⋅3 = 27. When the bases and the exponents are different we have to calculate each exponent and then divide: a n / b m.

What is the difference between a and an exponent?

Here a is any number and n is a natural number. an is also called the nth power of a. ‘a’ is the base and ‘n’ is the exponent or index or power. ‘a’ is multiplied ‘n’ times, and thereby exponentiation is the shorthand method of repeated multiplication. The laws of exponents are demonstrated based on the powers they carry.

What happens when you raise exponents to negative?

If a number is raised to negative exponents then it represents the reciprocal of it. For example, 3 raised to -2 is represented by 3 -2, which is equal to 1/3 2. What do we get if the exponent is 1 or 0? If the exponent of a base number is one, then the value of the base remains unchanged.

How do you add exponents in math?

Adding exponents is done by calculating each exponent first and then adding: The general form such exponents is: a n + b m. 6 2 + 6 3 = 252. 3 4 + 3 6 = 81 + 729 = 810.