base

$n$ is the index (or power/exponent)

","points":1},{"id":"19fa1350-252c-4993-b092-e95205e62b7b","cardType":"cloze","front":"The law for multiplying powers with the same base is $\\text{[...]}$.","back":"The law for multiplying powers with the same base is $\\boxed{a^m \\cdot a^n = a^{m+n}}$.","points":null},{"id":"fc358774-9217-4cbe-9903-9f415218acb9","cardType":"cloze","front":"The law for dividing powers with the same base is $\\text{[...]}$.","back":"The law for dividing powers with the same base is $\\boxed{\\frac{a^m}{a^n} = a^{m-n}}$.","points":null},{"id":"ff1c7734-885b-4c72-8e96-9d45c3767653","cardType":"cloze","front":"The law for a power of a power is $\\text{[...]}$.","back":"The law for a power of a power is $\\boxed{(a^m)^n = a^{mn}}$.","points":null},{"id":"53802db9-a9be-4de2-98b9-c87f0c4b2c47","cardType":"basic","front":"If $x = 2^p$ and $y = 2^q$, how is $2^{p+q}$ expressed in terms of $x$ and $y$?","back":"$$xy$","points":2},{"id":"2dffaeb1-a04d-4452-9d98-c948e0f31ece","cardType":"basic","front":"What does a negative index signify in mathematics?","back":"The reciprocal (1 divided by the base raised to the positive power).","points":1},{"id":"8db9f5c9-98aa-47f4-a6ff-4b6d33ced8fc","cardType":"cloze","front":"The general rule for negative indices is $\\text{[...]}$.","back":"The general rule for negative indices is $\\boxed{a^{-n} = \\frac{1}{a^n}}$.","points":null},{"id":"c2fcf51d-045d-4c9f-b9eb-86cfecbfa09c","cardType":"basic","front":"What is the value of $\\left(\\frac{3}{7}\\right)^{-1}$?","back":"$$\\frac{7}{3}$","points":1},{"id":"975d02c9-f60e-4ccd-9629-689fdd27006d","cardType":"basic","front":"Explain why $6^{-1}$ is not $-6$.","back":"A negative index represents a reciprocal, not a negative number; $6^{-1} = \\frac{1}{6}$.","points":2},{"id":"f4b03faa-e95c-4ce1-8ca7-f81b96ffa1d8","cardType":"basic","front":"Why is $0^{-1}$ undefined?","back":"It would require division by zero ($1/0$).","points":1},{"id":"3653a5b1-9976-4405-be65-a18f5ed55ef7","cardType":"basic","front":"What root corresponds to the index $\\frac{1}{2}$?","back":"Square root ($\\sqrt{a}$)","points":1},{"id":"e53303dc-c222-42d3-942e-cde7f400f916","cardType":"basic","front":"What root corresponds to the index $\\frac{1}{3}$?","back":"Cube root ($\\sqrt[3]{a}$)","points":1},{"id":"e5abab46-95c5-4353-b21a-2932276c78e1","cardType":"cloze","front":"For a fractional index $a^{\\frac{m}{n}}$, the denominator $n$ represents the [ ] and the numerator $m$ represents the power.","back":"For a fractional index $a^{\\frac{m}{n}}$, the denominator $n$ represents the root and the numerator $m$ represents the power.","points":null},{"id":"c8746431-1360-4167-aaf1-94dc38f8daa8","cardType":"cloze","front":"For a fractional index $a^{\\frac{m}{n}}$, the denominator $n$ represents the root and the numerator $m$ represents the [ ].","back":"For a fractional index $a^{\\frac{m}{n}}$, the denominator $n$ represents the root and the numerator $m$ represents the power.","points":null},{"id":"23d3eff0-c248-454e-bd7b-e452b124ad55","cardType":"basic","front":"When evaluating $a^{\\frac{m}{n}}$, why is it usually better to take the root first?","back":"It keeps the numbers smaller and easier to calculate before applying the power.","points":2},{"id":"38d6af1a-1886-468c-bdc9-779918f6b139","cardType":"basic","front":"Evaluate $27^{\\frac{2}{3}}$.","back":"

$\\sqrt[3]{27} = 3$
$3^2 = 9$

","points":2},{"id":"5b44ea46-c6d6-4bee-8049-478c838d6441","cardType":"basic","front":"Outline the 3 steps to evaluate $16^{-\\frac{3}{2}}$.","back":"

Square root: $\\sqrt{16} = 4$
Power: $4^3 = 64$
Reciprocal: $\\frac{1}{64

Fractional and Negative Indices Flashcards

Fractional and Negative Indices Flashcards

Fractional and Negative Indices Flashcards

Fractional and Negative Indices Flashcards