| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.91 |
| Score | 0% | 58% |
Which of the following statements about exponents is false?
b1 = 1 |
|
b1 = b |
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b0 = 1 |
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all of these are false |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
Find the average of the following numbers: 17, 13, 16, 14.
| 15 | |
| 14 | |
| 12 | |
| 19 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{17 + 13 + 16 + 14}{4} \) = \( \frac{60}{4} \) = 15
Convert b-5 to remove the negative exponent.
| \( \frac{-1}{-5b} \) | |
| \( \frac{-5}{-b} \) | |
| \( \frac{1}{b^5} \) | |
| \( \frac{-1}{b^{-5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( 3 \)\( \sqrt{75} \) - \( 5 \)\( \sqrt{3} \)
| -2\( \sqrt{-16} \) | |
| -2\( \sqrt{25} \) | |
| 10\( \sqrt{3} \) | |
| 15\( \sqrt{3} \) |
To subtract these radicals together their radicands must be the same:
3\( \sqrt{75} \) - 5\( \sqrt{3} \)
3\( \sqrt{25 \times 3} \) - 5\( \sqrt{3} \)
3\( \sqrt{5^2 \times 3} \) - 5\( \sqrt{3} \)
(3)(5)\( \sqrt{3} \) - 5\( \sqrt{3} \)
15\( \sqrt{3} \) - 5\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
15\( \sqrt{3} \) - 5\( \sqrt{3} \)What is -b6 + 2b6?
| b36 | |
| 3b-6 | |
| b6 | |
| -3b6 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-1b6 + 2b6
(-1 + 2)b6
b6