I don't understand how to solve the follow types of problems with exponets and fractions. If you explain with the examples provided that would be nice.
Ex. 1
4^-6 over 10
Ex. 2
6 over 9^-3
recall
x^-n = 1/x^2
then use the rules of regular fractions
I'll do the 2nd, you do the 1st in the same way:
6 over 9^-3
= 6/(9^-3)
but 9^-3 = 1/9^3 = 1/729
so 6/(9^-3) = 6 / (1/729)
= 6(729/1) = 4374
You can check these with your calculator, or google it
https://www.google.com/search?q=6%2F9%5E-3&rlz=1C5CHFA_enCA690CA690&oq=6%2F9%5E-3&aqs=chrome..69i57j6.6765j0j8&sourceid=chrome&ie=UTF-8
Thank you!
So...
(4^-6)/10
4^-6 = 1/4^6 = 4096
(1/4096) /10
1/40960
Did I do that right?
Sure! I'd be happy to explain how to solve problems with exponents and fractions using the examples you provided.
Example 1: 4^-6 over 10
To solve this problem, we need to perform two steps: simplify the exponent and then divide.
Step 1: Simplify the exponent
When a number is raised to a negative exponent, we can reciprocate the base (put it in the denominator) and change the exponent's sign to positive. In this case, 4^-6 becomes 1/4^6.
Step 2: Divide
Now, we have 1/4^6 over 10. To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the denominator fraction. So, we can rewrite the expression as (1/4^6) * 1/10.
Now, let's evaluate it:
1/4^6 = 1/4096 (since 4^6 = 4096)
So, the final simplified answer is (1/4096) * 1/10.
Example 2: 6 over 9^-3
Again, we will follow the same two steps: simplify the exponent and then divide.
Step 1: Simplify the exponent
In this case, 9^-3 becomes 1/9^3.
Step 2: Divide
Now, we have 6 over 1/9^3. To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the denominator fraction. So, we can rewrite the expression as 6 * 1/(1/9^3).
Now, let's evaluate it:
1/9^3 = 1/729 (since 9^3 = 729)
So, the final simplified answer is 6 * 1/729.
I hope this explanation helps you understand how to solve problems with exponents and fractions.