Simplifying Complex Expressions
Applying the rules for exponents to simplifying more complex expressions.
Subject: base
Transcript: DETERMINE THE SPEED OF THE CAR BASED ON THE LENGTH OF THE SKID MARKS. V STANDS FOR THE VELOCITY, OR SPEED OF THE CAR IN MILES PER HOUR. F IS THE COEFFICIENT
Simplifying An Expression Using Many Rules
Practice applying the rules for exponents to simplifying complex expressions.
Subject: base
Transcript: EXPONENTS OF B. WE STILL HAVE BASES THAT APPEAR MORE THAN ONCE. LOOK AT THE A'S. A TO THE 12TH OVER A CUBED IS A TO THE 9TH. NOW LOOK AT THE B'S. REMEMBER
Simplifying Expressions with Negative Exponents
Another expression is reduced to its simplest form, demonstrating the rule for dividing two monomials with the same base.
Subject: base
Transcript: WHAT IF OUR ORIGINAL EXPRESSION HAD BEEN Y SQUARED OVER Y TO THE SIXTH? THE RULE TELLS US TO SUBTRACT THE EXPONENTS. Y IS THE BASE, THE EXPONENT IS
Examples of Simplifying Expressions Written in Parentheses
Using more than one of the rules for exponents to simplify expressions written with parentheses.
Subject: base
Examples of Simplifying Expressions
Expressions that include a negative exponent can be simplified by first rewriting the expression with positive exponents.
Subject: base
Transcript: 1 IN THE DENOMINATOR OR WE CAN DROP IT. NOW WE CAN ADD THE EXPONENTS OF D. 2 PLUS 3 IS 5. THE ANSWER IS CD TO THE FIFTH. EACH BASE APPEARS ONLY ONCE
Multiplying Two Factors with the Same Base
The rules for exponents begin with the rule for multiplying two factors with the same base.
Subject: base
Transcript: FACTOR, X IS THE BASE. X SQUARED IS X TIMES X. X CUBED IS X TIMES X TIMES X. THE RESULT IS X MULTIPLIED BY ITSELF FIVE TIMES, SO WE CAN WRITE X TO THE
More than One Base Inside Parentheses
Simplifying an expression with more than one base contained within parentheses.
Subject: base
Transcript: SOMETIMES AN EXPRESSION IN PARENTHESES WILL INCLUDE MORE THAN ONE BASE. IN THIS EXPRESSION, 3 IS A BASE. SO IS X. THE PRODUCT OF 3 AND X IS RAISED
Fractions Raised to a Power
Simplifying expressions in which a fraction is raised to a power.
Subject: base
Transcript: QUANTITY A/B RAISED TO THE N EQUALS A TO THE N OVER B TO THE N. WE RAISE EACH BASE INSIDE OF THE PARENTHESES TO THE POWER OF THE EXPONENT OUTSIDE THE
Chemical Treatment Technologies: Chemical Principles
against potential dangers, treatment processes are being implemented to mitigate or eliminate the harmful effects of chemicals. These methods are based on
Subject: base
Transcript: processes are being implemented to mitigate... or eliminate the harmful effects of chemicals. these methods are based on the principles... that have been
Exponents Defined
A definition of exponents and their use.
Subject: base
Transcript: WRITE X TO THE FOURTH POWER. X IS THE BASE, POSITIVE 4 IS THE EXPONENT. THE EXPONENT GIVES US A SIMPLER WAY TO SHOW X MULTIPLIED BY ITSELF FOUR TIMES.