🟨 Index Laws Flashcards
(10 cards)
What is the zero index law?
Any non-zero number raised to the power of 0 is 1.
For example, a ^ 0 = 1
What is the negative index law?
A negative exponent means reciprocal.
For example, a ^ − n = 1 / a^n
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What are the main index laws?
a^m x a^n = a^m+n
a^m/a^n = a^m-n
(a^m)^n = a^mn
What is the product of powers rule for indices?
The product of powers rule states that when multiplying two powers with the same base, add the exponents:
a^m x a^n = a^m+n
How do you simplify expressions with multiple indices?
Use the index laws to combine terms.
For example:
a^m x a^n = a^m+n
a^m/a^n = a^m-n
(a^m)^n = a^mn
What does the power of a quotient rule state?
The power of a quotient rule states that when raising a fraction to a power, apply the power to both the numerator and the denominator:
(a/b)^n = a^n/b^n
Simplify the following expression using index laws:
x^3 x x^4
x^7
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Simplify the expression:
y^6/y^2
y^4
Simplify the expression:
(2x^3)^2
4x^6
Simplify:
a^-4/a^2
a^6
