Solve the following multiple choice arithmetic problems: 1. (-5/3)^(-1) = ? 2. (-1/2)^(3) = ? 3. (-3/4)^(2) = ? 4. 3670000 in standard form is 5. 0.0000463 in standard form is... Solve the following multiple choice arithmetic problems: 1. (-5/3)^(-1) = ? 2. (-1/2)^(3) = ? 3. (-3/4)^(2) = ? 4. 3670000 in standard form is 5. 0.0000463 in standard form is 6. 0.000367 x 10^4 in usual form is
Understand the Problem
The image contains a series of multiple-choice math questions. These questions cover topics such as exponents, fractions, and scientific notation. You need to solve each problem and choose the correct answer from the provided options.
Answer
12. (c) $-3/5$ 13. (d) $-1/8$ 14. (b) $9/16$ 15. (c) $3.67 \times 10^6$ 16. (b) $4.63 \times 10^{-5}$ 17. (a) $3.67$
Answer for screen readers
- (c) -3/5
- (d) -1/8
- (b) 9/16
- (c) 3.67x10^6
- (b) 4.63x10^-5
- (a) 3.67
Steps to Solve
- Question 12: Evaluate the exponent A negative exponent means taking the reciprocal of the base.
$(-5/3)^{-1} = -3/5$
- Question 13: Evaluate the exponent Apply the exponent to both the numerator and the denominator. Keep in mind that a negative number raised to an odd power is negative.
$(-1/2)^3 = (-1)^3 / (2)^3 = -1/8$
- Question 14: Evaluate the exponent Apply the exponent to both the numerator and the denominator. Keep in mind that a negative number raised to an even power is positive.
$(-3/4)^2 = (-3)^2 / (4)^2 = 9/16$
- Question 15: Convert to standard form Standard form requires writing the number as a value between 1 and 10 multiplied by a power of 10.
$3670000 = 3.67 \times 10^6$
- Question 16: Convert to standard form Move the decimal point until there is one non-zero digit to the left of the decimal point. The exponent of 10 will be the number of places the decimal point was moved. Since the original number is less than 1, the exponent will be negative.
$0.0000463 = 4.63 \times 10^{-5}$
- Question 17: Convert to usual form Convert from scientific notation to standard decimal notation.
$0.000367 \times 10^4 = 0.000367 \times 10000 = 3.67$
- (c) -3/5
- (d) -1/8
- (b) 9/16
- (c) 3.67x10^6
- (b) 4.63x10^-5
- (a) 3.67
More Information
Standard form is also known as scientific notation.
Tips
- Forgetting to apply the exponent to both the numerator and the denominator of a fraction.
- Incorrectly determining the sign of the result when raising a negative number to a power.
- Making errors when counting the number of decimal places to move when converting to/from scientific notation
- Not knowing that a negative exponent can be expressed as a positive exponent, by using the reciprocal (inverting the fraction).
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