In Simplifying 7 to the 11th power and 7 to the 9th power, Alexis decides to use her calculator to find 7 to the 11th power and 7 to the 9th power indiviually before dividing. Show how Alexis could use the laws of exponents to arrive at the answer more easily.
assume you are doing
7^11
------
7^9
Which is
7^9 * 7^2
----------
7^9
so 7^2
which is 49
to multiply, add exponents
to divide, subtract exponents
to raise to power, multiply exponents
thanks so much
You are welcome !
To simplify 7 to the 11th power and 7 to the 9th power using the laws of exponents, Alexis can use the rule for multiplying exponents when the base is the same.
First, let's look at 7 to the 11th power:
7 to the 11th power can be written as 7 multiplied by itself 11 times.
Instead of using a calculator to multiply 7 by itself 11 times, Alexis can simplify this expression using the exponent rule. The rule states that when multiplying two exponential expressions with the same base, we add the exponents.
Therefore, 7 to the 11th power can be simplified to 7 raised to the sum of its exponents, which is (11 + 9 = 20).
Next, let's look at 7 to the 9th power:
7 to the 9th power can be written as 7 multiplied by itself 9 times.
Applying the same exponent rule, we can simplify 7 to the 9th power to 7 raised to the sum of its exponents, which is (9 + 9 = 18).
Now, Alexis can divide the result of 7 to the 11th power (20) by the result of 7 to the 9th power (18) to find the simplified answer.