Laws of Indices Flashcards

All 6 cards in this deck

What is the multiplication law of indices?

e.g. $2^5 \times 2^4$

$a^m \times a^n = a^{m+n}$ (add the indices).
$2^5 \times 2^4 = 2^9$

What is the division law of indices?

e.g. $2^5 \div 2^3$

$a^m \div a^n = a^{m-n}$ (subtract the indices).
$2^5 \div 2^3 = 2^2$

What is the power law of indices?

e.g. $(2^3)^2$

$(a^m)^n = a^{mn}$ (multiply the indices).
$(2^3)^2 = 2^6$

What is the value of any non-zero number raised to the power $0$?

e.g. $7^0$

$1$
$7^0 = 1$

What does a negative index mean?

e.g. $5^{-2}$

$a^{-n} = \dfrac{1}{a^n}$ (the reciprocal).
$5^{-2} = \dfrac{1}{25}$

What are the steps to find a missing index?

e.g. $8^3 \times 8^x = 8^9$

1. Same base, so add the indices on the left: $3 + x$
2. Set the indices equal: $3 + x = 9$
3. Solve: $x = 6$