| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.37 |
| Score | 0% | 67% |
Convert b-3 to remove the negative exponent.
| \( \frac{1}{b^{-3}} \) | |
| \( \frac{-1}{-3b} \) | |
| \( \frac{3}{b} \) | |
| \( \frac{1}{b^3} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
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commutative property for division |
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distributive property for multiplication |
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commutative property for multiplication |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
What is 2b5 + 7b5?
| 9b25 | |
| 9b5 | |
| 9b10 | |
| 5b-5 |
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:
2b5 + 7b5
(2 + 7)b5
9b5
Which of these numbers is a factor of 28?
| 17 | |
| 2 | |
| 1 | |
| 6 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 28 are 1, 2, 4, 7, 14, 28.
Simplify \( \frac{24}{68} \).
| \( \frac{5}{8} \) | |
| \( \frac{10}{17} \) | |
| \( \frac{6}{17} \) | |
| \( \frac{1}{4} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{68} \) = \( \frac{\frac{24}{4}}{\frac{68}{4}} \) = \( \frac{6}{17} \)