Podcast
Questions and Answers
What is the result of raising the product of two numbers to a power?
What is the result of raising the product of two numbers to a power?
The product of the two numbers, each raised to that power.
Simplify the expression (2x)^3 using the power of a product law.
Simplify the expression (2x)^3 using the power of a product law.
2^3 * x^3 = 8x^3
What is the result of multiplying two powers of the same base?
What is the result of multiplying two powers of the same base?
A power of the same base with the sum of the exponents.
What is the result of dividing two powers of the same base?
What is the result of dividing two powers of the same base?
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Simplify the expression (x^2)^3 * x^4 using the product of powers law.
Simplify the expression (x^2)^3 * x^4 using the product of powers law.
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What is the equivalent expression for a^(-m)?
What is the equivalent expression for a^(-m)?
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If a and b are non-zero, and m is a real number, then (a/b)^m = a^m / b^m is an example of the ______ law.
If a and b are non-zero, and m is a real number, then (a/b)^m = a^m / b^m is an example of the ______ law.
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If a is non-zero, and m and n are real numbers, then a^m / a^n = a^(m-______).
If a is non-zero, and m and n are real numbers, then a^m / a^n = a^(m-______).
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The equation (ab)^m = a^m * b^m is an example of the ______ law.
The equation (ab)^m = a^m * b^m is an example of the ______ law.
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If a is non-zero, and m and n are real numbers, then a^m * a^n = a^(m+______).
If a is non-zero, and m and n are real numbers, then a^m * a^n = a^(m+______).
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The equation a^(-m) = 1 / a^m is an example of the ______ exponents law.
The equation a^(-m) = 1 / a^m is an example of the ______ exponents law.
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Study Notes
Exponent Laws
Power Of A Product
- If
aandbare non-zero numbers, andmis a real number, then:-
(ab)^m = a^m * b^m
-
- In other words, when a product is raised to a power, each factor is raised to that power.
Product Of Powers
- If
ais a non-zero number, andmandnare real numbers, then:-
a^m * a^n = a^(m+n)
-
- In other words, when two powers of the same base are multiplied, the exponents are added.
Power Of A Quotient
- If
aandbare non-zero numbers, andmis a real number, then:-
(a/b)^m = a^m / b^m
-
- In other words, when a quotient is raised to a power, the numerator and denominator are each raised to that power.
Quotient Of Powers
- If
ais a non-zero number, andmandnare real numbers, then:-
a^m / a^n = a^(m-n)
-
- In other words, when two powers of the same base are divided, the exponents are subtracted.
Negative Exponents
- If
ais a non-zero number, andmis a real number, then:-
a^(-m) = 1 / a^m
-
- In other words, a negative exponent is equivalent to the reciprocal of the positive exponent.
- For example,
2^(-3) = 1 / 2^3 = 1/8
Exponent Laws
Power of a Product
- When a product is raised to a power, each factor is raised to that power:
(ab)^m = a^m * b^m - This rule applies to non-zero numbers
aandb, and real numberm
Product of Powers
- When two powers of the same base are multiplied, the exponents are added:
a^m * a^n = a^(m+n) - This rule applies to non-zero number
a, and real numbersmandn
Power of a Quotient
- When a quotient is raised to a power, the numerator and denominator are each raised to that power:
(a/b)^m = a^m / b^m - This rule applies to non-zero numbers
aandb, and real numberm
Quotient of Powers
- When two powers of the same base are divided, the exponents are subtracted:
a^m / a^n = a^(m-n) - This rule applies to non-zero number
a, and real numbersmandn
Negative Exponents
- A negative exponent is equivalent to the reciprocal of the positive exponent:
a^(-m) = 1 / a^m - For example,
2^(-3) = 1 / 2^3 = 1/8 - This rule applies to non-zero number
a, and real numberm
Exponent Laws
Power Of A Quotient
-
(a/b)^m = a^m / b^m, whereaandbare non-zero andmis a real number.
Quotient Of Powers
-
a^m / a^n = a^(m-n), whereais non-zero andmandnare real numbers.
Power Of A Product
-
(ab)^m = a^m * b^m, whereaandbare non-zero andmis a real number.
Product Of Powers
-
a^m * a^n = a^(m+n), whereais non-zero andmandnare real numbers.
Negative Exponents
-
a^(-m) = 1 / a^m, whereais non-zero andmis a real number. -
1 / a^(-m) = a^m, whereais non-zero andmis a real number.
Applications
- Exponent laws can be used to simplify expressions and solve equations involving exponents.
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Description
Test your understanding of exponent laws including power of a product, product of powers, and power of a quotient.
