Dividing monomials
Summary
TLDRThe script explains the rules of exponents when dividing numbers with the same base. It highlights that exponents should be subtracted, and covers how to handle negative exponents by switching between numerator and denominator. The process involves reducing a fraction, applying exponent rules, and simplifying expressions. The final step is organizing the result, with the variables divided between numerator and denominator, following the rules of exponent manipulation.
Takeaways
- 🧮 Remember the rules of exponents: when dividing numbers with the same base, subtract the exponents.
- 🔢 When a number is raised to a negative exponent, you can rewrite it as 1 over the base raised to the positive exponent.
- ⚖️ A negative exponent in the denominator can be moved to the numerator by making it positive.
- ➗ Simplify fractions by reducing them, like reducing 6/3 to 2.
- 🔢 After reducing the numbers, apply exponent rules: subtract exponents when dividing bases with exponents.
- 🅰️ For variables without an exponent explicitly shown, assume the exponent is 1.
- 💡 Follow the operation: subtract exponents for each variable separately (e.g., a^4 / a^2 becomes a^2).
- ⚖️ Keep track of negative exponents, which may need to be moved to the denominator.
- 📉 After simplifying exponents, finalize the expression by placing negative exponents in the correct position (numerator or denominator).
- ✅ The final answer is a simplified expression with reduced coefficients and correctly placed exponents.
Q & A
What is the rule for dividing numbers with the same base and different exponents?
-When dividing numbers with the same base, you subtract the exponents. If both numbers have exponents, the result is the base raised to the difference of the exponents.
What happens when a number is raised to a negative exponent?
-When a number is raised to a negative exponent, it can be written as the reciprocal of the base raised to the positive of that exponent. For example, x^-m becomes 1/x^m.
How can a number in the denominator with a negative exponent be simplified?
-If a number in the denominator has a negative exponent, it can be moved to the numerator with the exponent made positive.
How do you simplify a fraction like 6/3 in an expression with exponents?
-You can simplify the fraction 6/3 by reducing it to 2/1 or simply 2. This step is independent of the exponents.
How do you simplify a term like a^4/a^2?
-To simplify a^4/a^2, subtract the exponents: 4 - 2 = 2. The result is a^2.
What happens when the exponent of a variable is missing or not explicitly written?
-If no exponent is shown for a variable, it is understood to have an exponent of 1.
How do you handle exponents in an expression like B^3/B^5?
-Subtract the exponents: 3 - 5 = -2. This result can be written as 1/B^2, moving the term to the denominator.
How do you simplify an expression with both numerator and denominator terms like a^2 * b^-2 * c^-2?
-Keep terms with positive exponents in the numerator and move terms with negative exponents to the denominator. The final result would be a^2 / (b^2 * c^2).
What does the speaker mean by '12 * a^2' in the final result?
-The speaker simplifies the original terms to combine constants and powers of variables, resulting in a coefficient of 12 multiplied by a^2.
What is the final simplified form of the expression according to the speaker?
-The final expression is a^2 / (2 * b^2 * c^2), where 12 was divided by 6 to give 2, and the variables were simplified based on exponent rules.
Outlines
📘 Exponents Rules and Division
The paragraph explains the rules for dividing numbers with exponents that share the same base. It emphasizes that when dividing such numbers, you subtract the exponents. The speaker also clarifies that a negative exponent can be represented as the reciprocal of the base raised to the positive exponent. The example provided involves simplifying a complex expression by reducing numbers and applying the exponent rules. The process results in a simplified expression where the exponents are subtracted, and the final answer is given in terms of the simplified base and exponents.
Mindmap
Keywords
💡Exponents
💡Division
💡Base
💡Negative Exponent
💡Reduction
💡Numerator
💡Denominator
💡Reciprocal
💡Multiplication
💡Simplification
Highlights
Remember the rules of exponents: when dividing numbers with the same base, subtract their exponents.
If a number is raised to a negative exponent, it can be written as 1 divided by that number raised to the positive exponent.
Similarly, if a negative exponent appears in the denominator, it can be moved to the numerator with a positive exponent.
To simplify fractions, reduce the numbers by dividing them; for example, 6 divided by 3 reduces to 2.
When dividing like bases, subtract the exponents: for instance, a^4 divided by a^2 results in a^2.
If there is no exponent shown for a variable, it is considered to be raised to the power of 1.
Example provided: a^4 / a^2 results in a^2.
Example provided: b^3 / b^5 results in b^(-2).
Example provided: c^1 / c^3 results in c^(-2).
Combining simplified terms: 12 * a^2 * b^(-2) * c^(-2).
Negative exponents in the final expression indicate they should be moved to the denominator.
Final result: a^2 / (2 * b^2 * c^2).
Explanation of why exponents are subtracted: due to the rules of division of powers.
Reaffirmation of moving negative exponents from numerator to denominator for simplification.
End confirmation that the mathematical process makes sense as demonstrated.
Transcripts
what's going to happen Okay so same
exact thing now what we want to do is
again we just want to remember our rules
of exponents our rules
of um a number with an exponent divided
by the same base of that number we're
going to take our exponents and as long
as they both have exponents we're going
to subtract the exponents okay okay and
obviously obviously they have same base
they're at least always going to have
the exponent um being up to one so we're
always going to be subtracting exponents
the next thing just remind you is if I
have a number raised to a negative
exponent we can put that as 1/ x to the
m and the same thing is if I have it as
a denominator that's negative I can put
it up as a numerator positive okay okay
so now we're just going to divide now
obviously not divide into three right
but what we can do is we can reduce this
so 6/3 can be reduced down to two or
one2 yeah one2
okay so I'm going to reduce that down to
1/2 and then I'm going to follow my
rules of exponents this is going to be a
4th over a 2 so I'm going to say a to 4
-
2 B to the 3 - 5 and C to the if there's
no exponent showing there we know that
it's C multiplied by itself one time
right C to the 1 minus 3 so now I just
have 12 * a 4 - 2 is a^ 2 B2 to
the2 -2 and then C to the2 now again
since these are two negatives I have to
be able to put them as the denominator
notice I have a numerator and
denominator so my two is going to join
them now with the at the denominator and
my a is going to stay up top as the
numerator so my final answer is all over
um 2 * b ^ 2 c^
2 okay yep makes sense
浏览更多相关视频
Kurikulum Merdeka Matematika Kelas 8 Bab 1 Bilangan Berpangkat
Asinkronus Topik Bentuk Akar W 2
POTENCIA DE UN EXPONENTE NEGATIVO Super facil - Para principiantes!!
Data Representation - Mantissa And Exponents Part 3 - (A Level Computer Science Made Easy (A2) )
Scientific Notation
Matematika Ekonomi - Pangkat, Akar dan Logaritma
5.0 / 5 (0 votes)