What is (6^2) (6^3)?
When multiplying together two numbers that are raised to a power but share the same base number (6 in this case) you can simply add the exponent numbers together and solve from there. So 6^2 x 6^3 = 6^(2+3) = 6^5 = 7776
What does it mean for something to be "to the power of something"?
To best explain the answer to this question we will go through an example together. Say we are trying to solve the answer to the following question... Q: What is 4 to the power of 2? A: 4^2 = (4) (4) = 16 When we set a number to the power of something that we are doing is multiplying that number by itself "something" amount of times. So 3 to the power of 4 would really be 3x3x3x3 and 4 to the power of 5 would be 4x4x4x4x4 and so on.
How can I use "substitution" to solve for x and y given the following equations? y=x+1 2y=3x
The first equation that we are provided within this problem gives us a value that is equal to "y". It does so by telling us that y is equal to (x+1). Since y and (x+1) are equal we can "substitute" by putting "x+1" in for y in the second equation. Doing so will give us the following... 2(x+1)=3x What that did for us was give us an equation with only one variable (x) rather than two (x and y). Now we will solve for x. 2x+2=3x 2=x now we take x=2 and replace the x in the first equation with 2 to solve for y y=2+1 y=3 So our final answer will be x=2, y=3