Explain how a factor tree helps you identify the base number and possible exponents in an expression.
a factor tree helps by the amount of number in the equation given that are the same. for example, 3*3*3= ?, this means 3 to the power of two since the number more than once in the equation is 3.
A factor tree is a visual representation used to break down a number into its prime factors. It can help us identify the base number and possible exponents in an expression because it allows us to see the prime factors and their corresponding exponents.
To create a factor tree, start by writing the given number at the top. Then, find two factors of the number that multiply together to give the original number. Write these two factors below the top number and draw a line connecting them. Continue this process for each subsequent factor, breaking down the numbers until you have only prime numbers at the bottom of the tree.
Once the factor tree is complete, you can identify the base number by multiplying all the prime factors together. The exponents can be determined by looking at the number of times each prime factor appears in the tree.
For example, let's say we have the expression 36 = 2^2 * 3^2. By constructing a factor tree, we would break down 36 into 2 * 18, then further into 2 * 2 * 9, and finally into 2 * 2 * 3 * 3. The base number is the product of all the prime factors (2 * 2 * 3 * 3 = 36), and the exponents are determined by counting the number of times each prime factor appears (2 appears twice, and 3 appears twice).
In summary, a factor tree helps us identify the base number by multiplying all the prime factors together and determine the exponents by analyzing the number of times each prime factor appears in the tree.