Exponents and Roots Practice Problems: GED Math

Answers

1. e.   7² = 7 × 7, and 7 × 7 = 49.
2. d.   When there is a negative exponent, take the reciprocal of the base and raise it to the positive power. 2–3, = , and .
3. b.   is the cube root of 27; what number multiplied by itself twice equals 27? Because 3 × 3 × 3 = 27, the answer is 3.
4. e.   An exponent of means the second root or square root of 25. Because 5 × 5 = 25, the answer is 5.
5. a.   When you multiply two numbers with the same base, you keep the base and add the exponents. 2² × 2³ = 2² + 3 = 2⁵.
6. c.   Ten with a negative exponent of 4 dictates that you move the decimal point four places to the left.
7. b.   Change the large number to be a decimal number between 1 and 10, followed by multiplication by a power of 10. By doing this, you have moved the decimal point eight places to the left.
8. c.   Divide: 5.4 ÷ 9 = 0.6. Then, use the law of exponents: 10¹⁶ ÷ 10¹⁴ = 10^{16 – 14} = 10². So this is 0.6 × 10² = 60 by moving the decimal point two places to the right.
9. d.   Evaluate the exponent first and then evaluate the negative sign: 5² = 5 × 5, which is 25, so the answer is –25.
10. c.   For order of operations, parentheses would have been evaluated first, but there are no parentheses. Evaluate exponents next to get 700 + 25 – 25 × 2. Multiplication is performed next: 700 + 25 – 50. Now, addition and subtraction are done left to right for a result of 725 – 50 = 675.

11. b.   For this problem, the exponent is handled first. Eleven squared is 11 times 11, which is 121, and then the negative sign is evaluated to get the answer of –121.
12. b.   The exponent of means the fourth root of 81; what factor multiplied by itself three times will yield 81? Trial and error will show that 3 × 3 × 3 × 3 = 81. The root is 3.
13. a.   The problem is asking for the cube root of 64; what number multiplied by itself twice will give the product of 64? Because 4 × 4 × 4 = 64, the cube root is 4.
14. a.   The problem is asking for the square root of 169. Because 13 times 13 equals 169, the root is 13.
15. c.   Combine these radicals by multiplying the radicands together: . The square root of 144 is 12, because 12 times 12 equals 144.
16. e.   Break this fractional radicand up into two separate radicals and then simplify what can be simplified. . The is simplified, and = 3. So, the answer is .
17. b.   The exponent of 7 on the power of 10 dictates that you move the decimal point in 2.701 seven places to the right. Three of the places will be taken up by the digits 7, 0, and 1, and then four more zeros will follow to result in 27,010,000.
18. c.   The negative exponent, –5, on the power of 10 means that you must move the decimal point five places to the left. The number 4.09 has only one digit to the left of the decimal point. Four leading zeros must be added as placeholders: 0.0000409.
19. c.   For this problem, you use the commutative and associative properties of multiplication and change the order of the factors to get (2.5 × 3.0) × (10^–4 × 10⁸). 2.5 times 3 equals 7.5. For the powers of 10, when you multiply two powers with the same base, you keep the base and add the exponents, which results in 10^–4 × 10⁸ = 10^–4 + 8 = 10⁴. Now, 7.5 × 10⁴ = 75,000 because you move the decimal point four places to the right, one place being the 5 (in the tenths place) followed by three trailing zeros for placeholders.
20. c.   First, perform the addition enclosed in the parentheses: 5 – (–10)2 × 3. Now, take negative 10 and square it, which is –10 × –10 = 100, so the problem becomes 5 – 100 × 3. Now, multiply: 5 – 300. Finally, subtract to get –295.