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50 Cards in this Set
- Front
- Back
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√1 |
1 |
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√2 |
1.4 |
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√3 |
1.7 |
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√5 |
2.25 |
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√169 |
13 |
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√196 |
14 |
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√225 |
15 |
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√256 |
16 |
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√400 |
20 |
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√625 |
25 |
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√900 |
30 |
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³√ 1 |
1 |
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³√ 8 |
2 |
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³√ 27 |
3 |
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³√ 64 |
4 |
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³√ 125 |
5 |
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1³ |
1 |
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2³ |
8 |
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3³ |
27 |
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4³ |
64 |
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5³ |
125 |
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1.4² |
2 |
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1.7² |
3 |
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2.25² |
5 |
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13² |
169 |
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14² |
196 |
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15² |
225 |
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16² |
256 |
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20² |
400 |
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25² |
625 |
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30² |
900 |
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What's dangerous about an even exponent? |
Hides the sign of the base |
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What is unique about a fractional base to the power of something? |
For fractions between 0 and 1 increasing powers causes the fractions to decrease. |
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0² |
0 |
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What can you do with a compound base? e.g. (2 * 5) ^3 |
You can multiply the base or distribute the exponent to each number. e.g. (10)^3 or 2^3 * 5^3.
NEVER do this with the sum of a base e.g. 2+5^3 |
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How do you simplify multiplying two terms with the same base? e.g. 3^4 * 3^2 |
Combine the exponents by adding. e.g. 3 ^ 6 |
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How do you simplify dividing two terms with the same base? e.g. 3 ^ 6 / 3 ^ 2 |
Combine the exponents by subtracting. e.g. 3 ^ 4 |
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How do you simplify a power to another power? e.g. (3^2)^4 |
Combine exponents by multiplying e.g. 3^8 |
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How do you simplify a power to a negative exponent? e.g. 5^(-1) |
Take the reciprocal e.g. 1/5 |
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How do you simplify a power of 0 |
Becomes 1 |
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How do you simplify a fractional exponent? e.g. 25^(3/2) |
Take the root of the denominator and the power of the numerator. e.g. (√25)^3 |
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When can you simplify exponential expressions? |
1. Linked by multiplication or division. You CANNOT if they're linked by addition or subtraction. 2. If linked by mult or division then they have to have either a base or an exponent in common |
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Simplify n√x * n√y |
n√xy |
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How do you estimate roots of imperfect squares? |
Find the two closest perfect squares on either side of it. Then figure which it's closer to. |
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Can even roots be positive and negative |
Even roots only have a positive value. |
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What steps should you take to simplify exponential expressions?
e.g. ((7^5 + 7^7)4^5)/ 8^3 * 25 |
4 step process. 1. Simplify or factor any additive or subtractive terms 2. Break every non-prime base down to prime factors 3. Distribute the exponents to every prime factor 4. Combine exponent for each prime factor and simplify
tl;dr make everything multiplied prime factors so they can be easily cancelled/combined |
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How should you simplify roots? e.g. simplify √180 |
1. Factor our primes for the number 2. Pull out pair of matching primes outside of the root 3. Consolidate |
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What's the difference between even and odd exponents? |
Even exponent make negative numbers become positive (so hide the sign). Odd exponents keep the sign. |
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What happens in the following scenarios when they are raised to a power greater than 1: Fraction (between 0 and 1) e.g. 1/2 ^ 3? 0 or 1? Number greater than 1? |
Fraction: Becomes smaller 0 or 1: Stays the same Greater than 1: Becomes larger |
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If xy = 0 what are the different scenarios? |
Either x or y is 0 Both x and y is 0 |
