Exponent Rules Unit Test Connexus
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Use the Product Rule of Exponents to simplify 5^10 ⋅ 5^5 (1 point)
Find the numerical equivalent of 9^9 ⋅ 9^−6 .(1 point)
What is the missing exponent in the following equation? h450/h? = h215 (1 point)
Simplify 12^87÷12^25 .(1 point)
What is the missing number in this simplified exponential expression: 7^?÷7^5=7^12 ?(1 point)
What is the value of 6.9−2^0 ?(1 point)
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0) .(2 points)
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What is the missing number in this simplified exponential expression: 7^?÷7^5=7^12 ?(1 point)
To find the missing number in the exponential expression 7^? ÷ 7^5 = 7^12, we can apply the quotient rule of exponents. According to the quotient rule, when dividing two exponential expressions with the same base, we subtract the exponents. Using this rule, we can rewrite the expression as:
7^(? - 5) = 7^12
For the two sides to be equal, the exponents must be the same. Therefore, we can set the exponent equation equal to 12:
? - 5 = 12
Solving for ?, we add 5 to both sides of the equation:
? = 12 + 5
? = 17
Therefore, the missing number in the simplified exponential expression is 17.
What is the value of 6.9−2^0 ?(1 point)
The value of 6.9 - 2^0 can be determined by evaluating the exponential expression first, as per the order of operations.
Since any number raised to the power of 0 equals 1, we have:
6.9 - 2^0 = 6.9 - 1
Simplifying further, we have:
6.9 - 1 = 5.9
Therefore, the value of 6.9 - 2^0 is 5.9.
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0) .(2 points)
The Zero Power Rule states that any non-zero number raised to the power of 0 is equal to 1. Therefore, we can simplify the expression using the Zero Power Rule.
9⋅(−33)^0+3/2(8−27^0)
Since (-33)^0 equals 1, we can substitute it in the expression:
9⋅1 + 3/2(8−1)
Simplifying further:
9 + 3/2(7)
Next, we evaluate 3/2(7):
3/2(7) = 21/2
Finally, we plug in the value:
9 + 21/2
The expression cannot be simplified any further. Therefore, the equivalent expression to 9⋅(−33)^0+3/2(8−27^0) is 9 + 21/2.
Solve the expression 15⋅8^0/5+4(7^0−6) .(1 point)
To solve the expression: 15⋅8^0/5+4(7^0−6), let's break it down step by step.
First, let's evaluate the exponential expressions:
8^0 = 1
7^0 = 1
Now, substitute these values back into the expression and simplify:
15⋅1/5 + 4(1 - 6)
Next, evaluate the subtraction within the parentheses:
15⋅1/5 + 4(-5)
Simplify further, performing multiplication and addition/subtraction:
3 + (-20) = -17
Therefore, the value of the expression 15⋅8^0/5+4(7^0−6) is -17.
Use the Power Rule of Exponents to simplify (10^3)^6 .(1 point)
The Power Rule of Exponents states that when raising a power to another power, you multiply the exponents.
In this case, we are raising 10^3 to the power of 6. Applying the Power Rule, we can simplify it as follows:
(10^3)^6 = 10^(3*6)
Multiplying the exponents, we get:
10^(18)
Thus, (10^3)^6 simplifies to 10^18.
If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)Responses
If the expression 7^15 is simplified using the Power Rule of Exponents, the expanded equivalent expression would be:
7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7
This represents multiplying 7 by itself 15 times, which is the expanded form of 7^15.
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9 .(1 point)
Using the Power Rule of Exponents, we can simplify the expression (19^4)^9 as follows:
(19^4)^9
Applying the Power Rule, we multiply the exponents:
19^(4 * 9)
Simplifying further, we have:
19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
Apply the Property of Negative Integer Exponents to solve 7^−3 . The answer should not contain any exponent expression or decimals.(1 point)
The Property of Negative Integer Exponents states that when a base is raised to a negative exponent, it can be rewritten as the reciprocal of the base raised to the positive exponent.
Using this property, we can solve 7^(-3) as follows:
7^(-3) = 1 / 7^3
The reciprocal of 7^3 is 1 divided by 7^3.
So, the solution to 7^(-3) is 1 / (7^3), which can be expressed as 1/343.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14 with positive exponents only.(1 point)
To apply the Property of Negative Integer Exponents and generate an expression with positive exponents only, we can rewrite 3^(-17) and 8^(-14) as reciprocals with positive exponents.
Using the property, we have:
3^(-17) = 1 / 3^17
8^(-14) = 1 / 8^14
Therefore, the expression 3^(-17) / 8^(-14) can be expressed as:
(1 / 3^17) / (1 / 8^14)
To simplify further, we can use the rule of dividing fractions, where the division of fractions is equivalent to multiplying by the reciprocal of the second fraction:
(1 / 3^17) * (8^14 / 1)
Now, we can simplify by multiplying the numerators and denominators together:
(8^14) / (3^17)
Therefore, the equivalent expression to 3^(-17) / 8^(-14) with positive exponents only is (8^14) / (3^17).
Apply the Properties of Integer Exponents to generate equivalent expressions to (7^−3)^7 ⋅ 7^20/6^−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can apply the following steps:
Step 1: Applying the property of negative exponents:
(7^(-3))^7 = 7^(-3 * 7) = 7^(-21)
(6^(-2)) = 1 / (6^2) = 1 / 36
Step 2: Applying the property of multiplying exponents:
(7^(-21)) ⋅ (7^20) = 7^(-21 + 20) = 7^(-1)
(7^(-1)) = 1 / (7^1) = 1/7
Step 3: Simplifying the expression:
(1/7) ⋅ (1/36) = 1 / (7 * 36) = 1 / 252
Therefore, the equivalent expression to (7^(-3))^7 ⋅ 7^20/6^(-2) with only positive exponents is 1 / 252.
u sure?
Apologies for the confusion in my previous response. Let's solve the expression correctly.
Given expression:
(7^(-3))^7 ⋅ 7^20/6^(-2)
Step 1: Simplify each part of the expression using the property of negative exponents:
(7^(-3))^7 = 7^(-3 * 7) = 7^(-21)
6^(-2) = 1 / 6^2 = 1 / 36
The expression becomes:
7^(-21) ⋅ 7^20 / 1/36
Step 2: Apply the property of multiplying exponents:
7^(-21) ⋅ 7^20 = 7^(-21 + 20) = 7^(-1)
7^(-1) = 1 / 7^1 = 1 / 7
Now the expression simplifies to:
1 / 7 ⋅ 1/36
Step 3: Simplify the multiplication:
(1 / 7) ⋅ (1/36) = 1 / (7 * 36) = 1 / 252
Therefore, the correct answer is 1/252 as an improper fraction.
wrong the answer is 36/7
Apologies for the incorrect response. Let's solve the expression again to obtain the correct answer.
Given expression:
(7^(-3))^7 ⋅ 7^20 / 6^(-2)
Let's simplify each part of the expression step by step:
Step 1: Apply the property of negative exponents:
(7^(-3))^7 = 7^(-3 * 7) = 7^(-21)
6^(-2) = 1 / 6^2 = 1 / 36
The expression becomes:
7^(-21) ⋅ 7^20 / 1/36
Step 2: Apply the property of multiplying exponents:
7^(-21) ⋅ 7^20 = 7^(-21 + 20) = 7^(-1)
7^(-1) = 1 / 7^1 = 1 / 7
Now the expression simplifies to:
1 / 7 ⋅ 1/36
Step 3: Simplify the multiplication:
(1 / 7) ⋅ (1/36) = 1 / (7 * 36) = 1 / 252
So the correct answer is indeed 1/252, and not 36/7. Apologies for the incorrect previous response.
Apply the product rule of integer exponents to find the numerical equivalent of 12^−5 ⋅ 12^7 . Show your work and explain how you used the product rule of integer exponents.(2 points)
To find the numerical equivalent of 12^(-5) ⋅ 12^7 using the product rule of integer exponents, we can apply the following steps:
Step 1: Apply the product rule of integer exponents, which states that when multiplying two exponential expressions with the same base, we add the exponents. So, 12^(-5) ⋅ 12^7 can be simplified as:
12^(-5 + 7)
Step 2: Simplify the exponent:
12^(2)
Therefore, the numerical equivalent of 12^(-5) ⋅ 12^7 is 12^2.
To calculate the value of 12^2, we multiply 12 by itself:
12^2 = 12 * 12 = 144
So, the numerical equivalent of 12^(-5) ⋅ 12^7 is 144.