Algebraic Roots & Indices Flashcards

All 9 cards in this deck

What is the law of indices for multiplying powers of the same letter?

e.g. $m^3 \times m^4$

$a^m \times a^n = a^{m+n}$ — add the indices.

$m^3 \times m^4 = m^7$

What is the law of indices for a power raised to another power?

e.g. $(d^4)^3$

$(a^m)^n = a^{mn}$ — multiply the indices.

$(d^4)^3 = d^{12}$

What are the steps to simplify a bracketed product raised to a power?

e.g. $(5np^3)^3$

1. Raise the number to the power: $5^3 = 125$
2. Multiply each letter's index by the power: $n^3$ and $p^{3\times3} = p^9$
3. Write as one product: $125n^3p^9$

True or false? $t \times t = 2t$

False. $t \times t = t^2$; it is $t + t$ that equals $2t$.

What is the law of indices for dividing powers of the same letter?

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

Subtract the indices: $a^m \div a^n = a^{m-n}$

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

True or false? $c^6 \div c^2 = c^3$

False. You subtract the indices, not divide them, so $c^6 \div c^2 = c^4$.

What are the steps to simplify a fraction whose top and bottom are each a single term (a number times powers)?

e.g. $\dfrac{12a^5b^3}{3a^2b}$

1. Divide the numbers: $12 \div 3 = 4$
2. Subtract the indices for each letter: $a^{5-2}=a^3$, $b^{3-1}=b^2$
3. Write as one product: $4a^3b^2$

In an algebraic fraction, what index does a letter written with no index have?

e.g. the $d$ on the bottom of $\dfrac{c^3d^4}{cd}$

$1$.

So $d^4 \div d^1 = d^3$.

True or false? $10^2 \times 10^3 = 100^5$

False. When multiplying powers the base stays the same, so $10^2 \times 10^3 = 10^5$.