We already realised with law 3 that a minus sign is another way of saying that the exponential number is to be divided instead of multiplied. Law 4 is just a more general way of saying the same thing. We get this law by multiplying law 3 by
on both sides and using law 2.
For example,
Application using exponential law 4:
Exponential law 5:
The order in which two real numbers are multiplied together does not matter. Therefore,
For example,
Application using exponential law 5:
Exponential law 6:
We can find the exponential of an exponential of a number. An exponential of a number is just a real number. So, even though the sentence sounds complicated, it is just saying that you can find the exponential of a number and then take the exponential of that number. You just take the exponential twice, using the answer of the first exponential as the argument for the second one.
For example,
Application using exponential law 6:
Simplify:
Investigation : exponential numbers
Match the answers to the questions, by filling in the correct answer into the
Answer column.
Possible answers are:
, 1,
,
, 8. Answers may be repeated.
Question
Answer
The following video gives an example on using some of the concepts covered in this chapter.
Summary
Exponential notation means a number written like
where
is an integer and
can be any real number.
is called the
base and
is called the
exponent or
index .
The
th power of
is defined as:
There are six laws of exponents:
Exponential Law 1:
Exponential Law 2:
Exponential Law 3:
Exponential Law 4:
Exponential Law 5:
Exponential Law 6:
End of chapter exercises
Simplify as far as possible:
Simplify without using a calculator. Leave your answers with positive exponents.
Simplify, showing all steps:
Simplify, without using a calculator:
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?