Podcast Beta
Questions and Answers
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.
2^3 * x^3 = 8x^3
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?
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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)?
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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.
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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.
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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.
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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.
