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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.
PropertyExample
x, start superscript, n, end superscript, dot, x, start superscript, m, end superscript, equals, x, start superscript, n, plus, m, end superscript2, 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 superscriptstart 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 superscriptleft 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 superscriptleft 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 fractionleft 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.
x, start superscript, n, end superscript, dot, x, start superscript, m, end superscript, equals, x, start superscript, n, plus, m, end superscript

Παράδειγμα

5, squared, dot, 5, start superscript, 5, end superscript, equals, 5, start superscript, 2, plus, 5, end superscript, equals, 5, start superscript, 7, end superscript

Εξάσκηση

Πρόβλημα 1.1
  • Τρέχων
Simplify.
Rewrite the expression in the form 8, start superscript, n, end superscript.
8, start superscript, 6, end superscript, dot, 8, start superscript, 4, end superscript, equals

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.
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

Παράδειγμα

start fraction, 3, start superscript, 8, end superscript, divided by, 3, squared, end fraction, equals, 3, start superscript, 8, minus, 2, end superscript, equals, 3, start superscript, 6, end superscript

Εξάσκηση

Πρόβλημα 2.1
  • Τρέχων
Simplify.
Rewrite the expression in the form 7, start superscript, n, end superscript.
start fraction, 7, start superscript, 7, end superscript, divided by, 7, cubed, end fraction, equals

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.
left parenthesis, x, start superscript, n, end superscript, right parenthesis, start superscript, m, end superscript, equals, x, start superscript, n, dot, m, end superscript

Παράδειγμα

left parenthesis, 8, squared, right parenthesis, cubed, equals, 8, start superscript, 2, dot, 3, end superscript, equals, 8, start superscript, 6, end superscript

Εξάσκηση

Πρόβλημα 3.1
  • Τρέχων
Simplify.
Rewrite the expression in the form 2, start superscript, n, end superscript.
left parenthesis, 2, start superscript, 4, end superscript, right parenthesis, squared, equals

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.
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

Παράδειγμα

left parenthesis, 3, dot, 5, right parenthesis, start superscript, 6, end superscript, equals, 3, start superscript, 6, end superscript, dot, 5, start superscript, 6, end superscript

Εξάσκηση

Πρόβλημα 4.1
  • Τρέχων
Select the equivalent expression.
left parenthesis, 4, dot, 7, right parenthesis, start superscript, 8, end superscript, equals, question mark
Επιλέξτε 1 απάντηση:

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.
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

Παράδειγμα

left parenthesis, start fraction, 7, divided by, 2, end fraction, right parenthesis, start superscript, 8, end superscript, equals, start fraction, 7, start superscript, 8, end superscript, divided by, 2, start superscript, 8, end superscript, end fraction

Εξάσκηση

Problem 5.1
  • Τρέχων
Select the equivalent expression.
left parenthesis, start fraction, 6, divided by, 5, end fraction, right parenthesis, start superscript, 9, end superscript, equals, question mark
Επιλέξτε 1 απάντηση:

Want to try more problems like these? Check out this exercise.

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