Which of the following expressions can be simplified to give an answer of 1?
To determine which of the expressions can be simplified to give an answer of 1, let's evaluate each expression:
1. (2 - 1) + (3 - 2)
Simplifying this expression step by step:
(2 - 1) + (3 - 2)
1 + (3 - 2)
1 + 1
The answer is 2, not 1. This expression cannot be simplified to give an answer of 1.
2. (5 - 3) × (2 - 1)
Simplifying this expression step by step:
(5 - 3) × (2 - 1)
2 × (2 - 1)
2 × 1
The answer is 2, not 1. This expression cannot be simplified to give an answer of 1.
3. (4 - 3) ÷ (2 - 1)
Simplifying this expression step by step:
(4 - 3) ÷ (2 - 1)
1 ÷ (2 - 1)
1 ÷ 1
The answer is 1. This expression simplifies to give an answer of 1.
Therefore, option 3: (4 - 3) ÷ (2 - 1) is the expression that can be simplified to give an answer of 1.
Which of the following expressions can be simplified to give an answer of 1?
11^0+24^0
15−(9.1)^0
2(8^0)
(−5.22)^0
To determine which of the expressions can be simplified to give an answer of 1, let's evaluate each expression:
1. 11^0 + 24^0
Any number raised to the power of 0 equals 1, so both terms in this expression will be 1.
Therefore, 11^0 + 24^0 simplifies to 1 + 1 = 2. This expression does not simplify to give an answer of 1.
2. 15 - (9.1)^0
Again, any number raised to the power of 0 equals 1. So, (9.1)^0 = 1.
Therefore, 15 - (9.1)^0 simplifies to 15 - 1 = 14. This expression does not simplify to give an answer of 1.
3. 2(8^0)
Once again, any number raised to the power of 0 equals 1. So, 8^0 = 1.
Therefore, 2(8^0) simplifies to 2(1) = 2. This expression does not simplify to give an answer of 1.
4. (-5.22)^0
Similarly, any number raised to the power of 0 equals 1. So, (-5.22)^0 = 1.
Therefore, (-5.22)^0 simplifies to 1. This expression does simplify to give an answer of 1.
Therefore, the expression (−5.22)^0 can be simplified to give an answer of 1.
Use the Power Rule of Exponents to simplify the expression
(x^6)^5
The Power Rule of Exponents states that when you raise a power to another power, you multiply the exponents.
Using this rule, let's simplify the expression (x^6)^5:
(x^6)^5 = x^(6 * 5) = x^30
Therefore, the expression (x^6)^5 simplifies to x^30.
If the expression 5^10
was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?
If the expression 5^10 is simplified using the Power Rule of Exponents, the expanded equivalent expression would be:
5^10 = 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 = 9,765,625
Therefore, the expanded equivalent expression is 9,765,625.
If the expression 5^10
was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses
(5^16)^6
open paren 5 to the 16th power close paren to the 6th power
(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)
(5⋅5)^8
r
(5⋅5)⋅(5⋅5)⋅(5⋅5)⋅(5⋅5)⋅(5⋅5)
If the expression 5^10 is simplified using the Power Rule of Exponents, the expanded equivalent expression would be:
(5^10) = (5^2)^5 = (5 * 5)^5 = (25)^5
Therefore, the expanded equivalent expression is (25)^5.
If the expression 5^10
was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses
(5^16)^6
(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)
(5⋅5)^8
(5⋅5)⋅(5⋅5)⋅(5⋅5)⋅(5⋅5)⋅(5⋅5)
If the expression 5^10 is simplified using the Power Rule of Exponents, the expanded equivalent expression would be:
(5^10) = (5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5) = 9,765,625
Therefore, the expanded equivalent expression is (5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5).
Which of the following is equivalent to 3^−4
To find the equivalent expression of 3^(-4), we can use the rule that states a negative exponent is the reciprocal of the positive exponent:
3^(-4) = 1 / 3^4
Therefore, the expression 3^(-4) is equivalent to 1 / 3^4.
Apply the Property of Negative Integer Exponents to find the numerical equivalent of 8^−3
. The answer should not contain any exponent expression or decimals
To find the numerical equivalent of 8^(-3) using the property of negative integer exponents, we can rewrite it as the reciprocal of 8^3:
8^(-3) = 1 / 8^3
Now, let's calculate 8^3 to determine the reciprocal:
8^3 = 8 * 8 * 8 = 512
So, the reciprocal of 8^3 is 1/512.
Therefore, the numerical equivalent of 8^(-3) is 1/512.
Complete the table. For each of the expressions, choose which exponent rule has been used to simplify.
(16^3)^9= 16^27
6^−12/9−^15=9^15/6^12
11^80/11^22=11^58
To complete the table, we need to identify which exponent rule has been used to simplify each expression:
Expression: (16^3)^9
Simplification: (16^3)^9 = 16^27
Exponent Rule: Power of a Power Rule
Expression: 6^(-12) / 9^(-15)
Simplification: 6^(-12) / 9^(-15) = 9^15 / 6^12
Exponent Rule: Negative Exponent Rule (reciprocal)
Expression: 11^80 / 11^22
Simplification: 11^80 / 11^22 = 11^58
Exponent Rule: Power of a Quotient Rule
Therefore, the table can be completed as follows:
____________________________________________________________________
| Expression | Simplified Form | Exponent Rule |
|__________________|________________|_________________________________|
| (16^3)^9 | 16^27 | Power of a Power Rule |
| 6^(-12) / 9^(-15)| 9^15 / 6^12 | Negative Exponent Rule (reciprocal) |
| 11^80 / 11^22 | 11^58 | Power of a Quotient Rule |
|__________________|________________|_________________________________|
Apply the Properties of Integer Exponents to generate an equivalent expression to (5^−3)^6⋅ 5^17/10^−2
with only positive exponents, then solve the expression. (1 point)
To generate an equivalent expression with only positive exponents, we can use the following properties of integer exponents:
1. Property: (a^m)^n = a^(m * n)
2. Property: a^(-n) = 1 / a^n
3. Property: a^m / a^n = a^(m - n)
Let's apply these properties to the given expression:
(5^(-3))^6 * 5^17 / 10^(-2)
Using the Property 1, we have:
(5^(-3))^6 = 5^(-3 * 6) = 5^(-18)
Applying Property 2, we simplify:
5^(-18) = 1 / 5^18
Now, let's simplify the entire expression:
(1 / 5^18) * 5^17 / 10^(-2)
Using Property 3 to divide the exponents:
5^17 / 5^18 * 10^2
Simplifying further:
1 / 5^(18 - 17) * 10^2
1 / 5^1 * 100
1 / 5 * 100
20
Therefore, the final simplified expression is 20.
Select all terms that are equivalent to 4^3/4^5
To determine which terms are equivalent to 4^3/4^5, we can simplify the expression using the exponent rule for division:
4^3/4^5 = 4^(3-5) = 4^(-2) = 1/4^2 = 1/16
Therefore, the term 1/16 is equivalent to 4^3/4^5.
Complete the table. For each statement, select True or False.(2 points)
True False
6^3 ⋅ 6^5=6^15
5^11/5^−7=5^18
(9^−7)^0 =1
To complete the table, we need to determine whether each statement is True or False:
Statement: 6^3 * 6^5 = 6^15
Solution: This statement is False. The correct simplification would be:
6^3 * 6^5 = 6^(3 + 5) = 6^8
Statement: 5^11 / 5^(-7) = 5^18
Solution: This statement is True. When we divide two terms with the same base, we subtract the exponents:
5^11 / 5^(-7) = 5^(11 - (-7)) = 5 ^ 18
Statement: (9^(-7))^0 = 1
Solution: This statement is True. Any non-zero number raised to the power of 0 is equal to 1.
Therefore, the completed table would be:
____________________________________________________________________
| Statement | True | False |
|__________________________|________________|________________________________|
| 6^3 * 6^5 = 6^15 | False | True |
| 5^11 / 5^(-7) = 5^18 | True | False |
| (9^(-7))^0 = 1 | True | False |
|__________________________|________________|________________________________|