Κύριο περιεχόμενο
8η τάξη
Course: 8η τάξη > Ενότητα 1
Μάθημα 5: Exponent properties intro- Exponent properties with products
- Exponent properties with parentheses
- Δυνάμεις των δυνάμεων
- Exponent properties with quotients
- Διαίρεση δυνάμεων
- Powers of products & quotients (structured practice)
- Powers of products & quotients
- Exponent properties review
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Exponent properties review
Review the common properties of exponents that allow us to rewrite powers in different ways. For example, x²⋅x³ can be written as x⁵.
| Property | Example |
|---|---|
| x, start superscript, n, end superscript, dot, x, start superscript, m, end superscript, equals, x, start superscript, n, plus, m, end superscript | 2, cubed, dot, 2, start superscript, 5, end superscript, equals, 2, start superscript, 8, end superscript |
| start fraction, x, start superscript, n, end superscript, divided by, x, start superscript, m, end superscript, end fraction, equals, x, start superscript, n, minus, m, end superscript | start fraction, 3, start superscript, 8, end superscript, divided by, 3, squared, end fraction, equals, 3, start superscript, 6, end superscript |
| left parenthesis, x, start superscript, n, end superscript, right parenthesis, start superscript, m, end superscript, equals, x, start superscript, n, dot, m, end superscript | left parenthesis, 5, start superscript, 4, end superscript, right parenthesis, cubed, equals, 5, start superscript, 12, end superscript |
| left parenthesis, x, dot, y, right parenthesis, start superscript, n, end superscript, equals, x, start superscript, n, end superscript, dot, y, start superscript, n, end superscript | left parenthesis, 3, dot, 5, right parenthesis, start superscript, 7, end superscript, equals, 3, start superscript, 7, end superscript, dot, 5, start superscript, 7, end superscript |
| left parenthesis, start fraction, x, divided by, y, end fraction, right parenthesis, start superscript, n, end superscript, equals, start fraction, x, start superscript, n, end superscript, divided by, y, start superscript, n, end superscript, end fraction | left parenthesis, start fraction, 2, divided by, 3, end fraction, right parenthesis, start superscript, 5, end superscript, equals, start fraction, 2, start superscript, 5, end superscript, divided by, 3, start superscript, 5, end superscript, end fraction |
Want to learn more about these properties? Check out this video and this video.
Product of powers
This property states that when multiplying two powers with the same base, we add the exponents.
Παράδειγμα
Εξάσκηση
Want to try more problems like these? Check out this exercise.
Quotient of powers
This property states that when dividing two powers with the same base, we subtract the exponents.
Παράδειγμα
Εξάσκηση
Want to try more problems like these? Check out this exercise.
Power of a power property
This property states that to find a power of a power we multiply the exponents.
Παράδειγμα
Εξάσκηση
Want to try more problems like these? Check out this exercise.
Power of a product
This property states that when taking the power of a product, we multiply the powers of the factors.
Παράδειγμα
Εξάσκηση
Want to try more problems like these? Check out this exercise.
Power of a quotient
This property states that when taking the power of a quotient, we divide the powers of the numerator and of the denominator.
Παράδειγμα
Εξάσκηση
Want to try more problems like these? Check out this exercise.
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