Exponential Expressions
1. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
A.
B.
C.
D.
2. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
A.
B.
C.
D.
3. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
A.
B.
C.
D.
4. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
1015 × 10-2
A. 1710
B. 1310
C. 1013
D. 1017
5. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
(54)5 ÷ 54
A. 5
B. 55
C. 516
D. 524
6. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
(45)7 ÷ 435
A.
B.
C.
D.
8. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
A.
B.
C.
D.
9. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
(34)6 ÷ 35
A. 329
B. 319
C. 35
D. 3
10. For all real numbers a, m, and n, the following statements are true.
Use any of the properties given above to find an expression equivalent to the one shown below.
(34)8 ÷ 332
A.
B.
C.
D.
Answers
1. A
2. A
3. B
4. C
5. C
6. A
8. B
9. B
10. C
Explanations
1. Whenever an exponent is raised to a power, multiply the exponent and power together.
When dividing two or more exponential expressions with the same base, subtract the exponents.
A number raised to a negative exponent is equivalent to its reciprocal but with a positive
exponent.
2. Whenever an exponent is raised to a power, multiply the exponent and power together.
When multiplying two or more exponential expressions with the same base, add the exponents.
A number raised to a negative exponent is equivalent to its reciprocal but with a positive
exponent.
3. Whenever an exponent is raised to a power, multiply the exponent and power together.
When dividing two or more exponential expressions with the same base, subtract the exponents.
A number raised to a negative exponent is equivalent to its reciprocal but with a positive
exponent.
4. When multiplying two or more exponential expressions with the same base, add the
exponents.
am × an = a(m + n)
1015 × 10-2 = 10(15 + (-2))
= 1013
5. Whenever an exponent is raised to a power, multiply the exponent and power together.
(am)n = a(m × n)
(54)5 = 5(4 × 5)
= 520
When dividing two or more exponential expressions with the same base, subtract the exponents.
am ÷ an = a(m - n)
520 ÷ 54 = 5(20 - 4)
= 516
6. Whenever an exponent is raised to a power, multiply the exponent and the power together.
(am)n = a(m × n)
(45)7 = 4(5 × 7)
= 435
When dividing two or more exponential expressions with the same base, subtract the exponents.
am ÷ an = a(m - n)
435 ÷ 435 = 4(35 - 35)
= 40
Any number raised to the zero power is equal to 1.
40 = 1
7.
First, recall these rules when simplifying exponential expressions.
When multiplying two exponential expressions that have the same base, add the exponents.
When dividing two exponential expressions that have the same base, subtract the exponents.
When an exponent is raised to a power, multiply the exponent and the power together.
When a number is raised to a negative exponent, it is equivalent to its reciprocal but with a
positive exponent.
Next, simplify each expression.
For the expression
For the expression
For the expression
, simplify the first term, and then divide the two expressions.
, simplify the first term, and then divide the two expressions.
, multiply the two expressions.
Therefore, the expressions in order from least value to greatest value are shown below.
<
<
8. Whenever an exponent is raised to a power, multiply the exponent and power together.
When multiplying two or more exponential expressions with the same base, add the exponents.
A number raised to a negative exponent is equivalent to its reciprocal but with a positive
exponent.
9. Whenever an exponent is raised to a power, multiply the exponent and power together.
(am)n = a(m × n)
(34)6 = 3(4 × 6)
= 324
When dividing two or more exponential expressions with the same base, subtract the exponents.
am ÷ an = a(m - n)
324 ÷ 35 = 3(24 - 5)
= 319
10. Whenever an exponent is raised to a power, multiply the exponent and the power together.
(am)n = a(m × n)
(34)8 = 3(4 × 8)
= 332
When dividing two or more exponential expressions with the same base, subtract the exponents.
am ÷ an = a(m - n)
332 ÷ 332 = 3(32 - 32)
= 30
Any number raised to the zero power is equal to 1.
30 = 1