The product rule of exponents states that when multiplying two powers with the same base, you add the exponents.
In this case, we have 5^10 * 5^5. Using the product rule of exponents, we add the exponents together: 10 + 5 = 15.
Therefore, 5^10 * 5^5 simplifies to 5^15.
The correct answer is D. 5^15.
Use the Product Rule of Exponents to simplify 5^10 * 5^5
A. 25^50
B. 5^50
C. 25^15
D. 5^15
29 answers
Find the numerical equivalent of 9^9 * 9^-6
To find the numerical equivalent of 9^9 * 9^-6, we can simplify this expression using the product rule of exponents.
The product rule of exponents states that when multiplying two powers with the same base, you add the exponents.
In this case, the base is 9. So, using the product rule of exponents, we add the exponents together: 9 + (-6) = 3.
Therefore, 9^9 * 9^-6 simplifies to 9^3.
To find the numerical equivalent of 9^3, we can calculate it by multiplying 9 by itself three times: 9 * 9 * 9 = 729.
Therefore, the numerical equivalent of 9^9 * 9^-6 is 729.
The product rule of exponents states that when multiplying two powers with the same base, you add the exponents.
In this case, the base is 9. So, using the product rule of exponents, we add the exponents together: 9 + (-6) = 3.
Therefore, 9^9 * 9^-6 simplifies to 9^3.
To find the numerical equivalent of 9^3, we can calculate it by multiplying 9 by itself three times: 9 * 9 * 9 = 729.
Therefore, the numerical equivalent of 9^9 * 9^-6 is 729.
What is the missing exponent in the following equation?
h^450/h^? = h^215
h^450/h^? = h^215
To find the missing exponent in the equation h^450/h^? = h^215, we can use the quotient rule of exponents.
The quotient rule of exponents states that when dividing two powers with the same base, you subtract the exponents.
In this case, the base is h.
Using the quotient rule of exponents, we subtract the exponents: 450 - ? = 215.
To solve for the missing exponent, we need to isolate the variable "?". We can start by subtracting 215 from both sides of the equation: 450 - 215 = ?.
This simplifies to 235 = ?.
Therefore, the missing exponent in the equation h^450/h^? = h^215 is 235.
The quotient rule of exponents states that when dividing two powers with the same base, you subtract the exponents.
In this case, the base is h.
Using the quotient rule of exponents, we subtract the exponents: 450 - ? = 215.
To solve for the missing exponent, we need to isolate the variable "?". We can start by subtracting 215 from both sides of the equation: 450 - 215 = ?.
This simplifies to 235 = ?.
Therefore, the missing exponent in the equation h^450/h^? = h^215 is 235.
Simplify 12^87 / 12^25
To simplify 12^87 / 12^25, we can use the quotient rule of exponents.
The quotient rule of exponents states that when dividing two powers with the same base, you subtract the exponents.
In this case, the base is 12.
Using the quotient rule of exponents, we subtract the exponents: 87 - 25 = 62.
Therefore, 12^87 / 12^25 simplifies to 12^62.
The quotient rule of exponents states that when dividing two powers with the same base, you subtract the exponents.
In this case, the base is 12.
Using the quotient rule of exponents, we subtract the exponents: 87 - 25 = 62.
Therefore, 12^87 / 12^25 simplifies to 12^62.
What is the missing number in this simplified exponential expression;
7^? / 7^5 = 7^12?
7^? / 7^5 = 7^12?
To find the missing number in the expression 7^? / 7^5 = 7^12?, we can use the quotient rule of exponents.
The quotient rule of exponents states that when dividing two powers with the same base, you subtract the exponents.
In this case, the base is 7.
Using the quotient rule of exponents, we subtract the exponents: ? - 5 = 12?.
To solve for the missing number, we need to isolate the variable "?". We can start by subtracting 12? from both sides of the equation: ? - 12? = 5.
This simplifies to -11? = 5.
To solve for "?", we divide both sides of the equation by -11: ? = -5/11.
Therefore, the missing number in the expression 7^? / 7^5 = 7^12? is -5/11.
The quotient rule of exponents states that when dividing two powers with the same base, you subtract the exponents.
In this case, the base is 7.
Using the quotient rule of exponents, we subtract the exponents: ? - 5 = 12?.
To solve for the missing number, we need to isolate the variable "?". We can start by subtracting 12? from both sides of the equation: ? - 12? = 5.
This simplifies to -11? = 5.
To solve for "?", we divide both sides of the equation by -11: ? = -5/11.
Therefore, the missing number in the expression 7^? / 7^5 = 7^12? is -5/11.
What is the value of 6.9 - 2^0?
A. 6.9
B. 7.9
C. 4.9
D. 5.9
A. 6.9
B. 7.9
C. 4.9
D. 5.9
The value of 2^0 is 1, as any number raised to the power of 0 equals 1.
Therefore, 6.9 - 2^0 simplifies to 6.9 - 1.
Calculating the subtraction gives us 5.9.
The correct answer is D. 5.9.
Therefore, 6.9 - 2^0 simplifies to 6.9 - 1.
Calculating the subtraction gives us 5.9.
The correct answer is D. 5.9.
Apply the Zero Power Rule to create an equivalent expression to 9 * (-33)^0 + 8/2 (8-27^0)
9 * (-33)^0 + 3/2 (8 - 27^0) = _ * _ + 3/2(_ - _)
9 * (-33)^0 + 3/2 (8 - 27^0) = _ * _ + 3/2(_ - _)
To apply the Zero Power Rule, any number raised to the power of 0 equals 1.
In this case, applying the Zero Power Rule to (-33)^0 gives us 1.
The expression 9 * (-33)^0 becomes 9 * 1.
To simplify further, 9 * 1 is just 9.
Therefore, 9 * (-33)^0 simplifies to 9.
The given expression can be rewritten as:
9 + 3/2(8 - 27^0) = 9 + 3/2(8 - 1)
The expression simplifies to:
9 + 3/2(7)
The equivalent expression to 9 * (-33)^0 + 3/2(8 - 27^0) is 9 + 3/2(7).
In this case, applying the Zero Power Rule to (-33)^0 gives us 1.
The expression 9 * (-33)^0 becomes 9 * 1.
To simplify further, 9 * 1 is just 9.
Therefore, 9 * (-33)^0 simplifies to 9.
The given expression can be rewritten as:
9 + 3/2(8 - 27^0) = 9 + 3/2(8 - 1)
The expression simplifies to:
9 + 3/2(7)
The equivalent expression to 9 * (-33)^0 + 3/2(8 - 27^0) is 9 + 3/2(7).
Solve the expression 15 * 8^0/5 + 4 (7^0 - 6)
15 * 8^0/5 + 4 (7^0 - 6) = _
15 * 8^0/5 + 4 (7^0 - 6) = _
To solve the given expression 15 * 8^0/5 + 4 (7^0 - 6), we'll follow the order of operations (PEMDAS).
First, we simplify any exponents:
- Since 8^0 is equal to 1, the expression becomes 15 * 1/5 + 4(1 - 6).
Next, we perform any multiplications:
- 15 * 1/5 gives us 3 + 4(1 - 6).
Now, we simplify the subtraction:
- 1 - 6 equals -5, so the expression becomes 3 + 4(-5).
Finally, we perform the multiplication:
- 4(-5) equals -20, leaving us with 3 + (-20).
Simplifying further:
- 3 + (-20) is the same as 3 - 20, which equals -17.
Therefore, the value of the expression 15 * 8^0/5 + 4 (7^0 - 6) is -17.
First, we simplify any exponents:
- Since 8^0 is equal to 1, the expression becomes 15 * 1/5 + 4(1 - 6).
Next, we perform any multiplications:
- 15 * 1/5 gives us 3 + 4(1 - 6).
Now, we simplify the subtraction:
- 1 - 6 equals -5, so the expression becomes 3 + 4(-5).
Finally, we perform the multiplication:
- 4(-5) equals -20, leaving us with 3 + (-20).
Simplifying further:
- 3 + (-20) is the same as 3 - 20, which equals -17.
Therefore, the value of the expression 15 * 8^0/5 + 4 (7^0 - 6) is -17.
1Use the Power Rule of Exponents to simplify (10^3)^6
The Power Rule of Exponents states that when raising an exponent to another exponent, you multiply the exponents.
In this case, we have (10^3)^6.
Using the Power Rule of Exponents, we multiply the exponents: 3 * 6 = 18.
Therefore, (10^3)^6 simplifies to 10^18.
In this case, we have (10^3)^6.
Using the Power Rule of Exponents, we multiply the exponents: 3 * 6 = 18.
Therefore, (10^3)^6 simplifies to 10^18.
If this expression 7^15 was simplified using Power Rule of Exponents, which of the following would be an expanded equivalent expression?
A. (7*7*7) * (7*7*7) * (7*7*7) * (7*7*7) * (7*7*7)
B. (7^18)^3
C. (7*7*7*7*7)^10
D. (7^10)^5
A. (7*7*7) * (7*7*7) * (7*7*7) * (7*7*7) * (7*7*7)
B. (7^18)^3
C. (7*7*7*7*7)^10
D. (7^10)^5
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).
This expanded expression can be rearranged as (7^15).
Therefore, the correct answer is D. (7^10)^5.
This expanded expression can be rearranged as (7^15).
Therefore, the correct answer is D. (7^10)^5.
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9
To create a simplified equivalent expression for (19^4)^9 using the Power Rule of Exponents, we multiply the exponents.
The Power Rule of Exponents states that when raising an exponent to another exponent, you multiply the exponents.
In this case, we have (19^4)^9.
Using the Power Rule of Exponents, we multiply the exponents: 4 * 9 = 36.
Therefore, (19^4)^9 simplifies to 19^36.
The Power Rule of Exponents states that when raising an exponent to another exponent, you multiply the exponents.
In this case, we have (19^4)^9.
Using the Power Rule of Exponents, we multiply the exponents: 4 * 9 = 36.
Therefore, (19^4)^9 simplifies to 19^36.
Apply the Property of Negative Integer Exponents to solve 7^-3. The answer should not contain any exponent expression or decimals
7^-3 = _
7^-3 = _
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.
In this case, 7^-3 can be rewritten as 1/7^3.
Now, we can simplify 1/7^3. To calculate 7^3, we multiply 7 by itself three times: 7 * 7 * 7 = 343.
Therefore, 7^-3 simplifies to 1/343.
The answer is 1/343.
In this case, 7^-3 can be rewritten as 1/7^3.
Now, we can simplify 1/7^3. To calculate 7^3, we multiply 7 by itself three times: 7 * 7 * 7 = 343.
Therefore, 7^-3 simplifies to 1/343.
The answer is 1/343.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^-17/8^-14 with positive exponents only
Sorry, there was a mistake in the initial expression. Let's correct it.
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.
In this case, we have 3^-17/8^-14.
Using the Property of Negative Integer Exponents, we can rewrite the expression as 1/(3^17) * (8^14).
Now, to generate an expression with positive exponents only, we can rewrite (8^14) as (1/8^14).
Substituting this back into the expression, we have 1/(3^17) * (1/8^14).
Therefore, the expression equivalent to 3^-17/8^-14 with positive exponents only is 1/(3^17) * (1/8^14).
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.
In this case, we have 3^-17/8^-14.
Using the Property of Negative Integer Exponents, we can rewrite the expression as 1/(3^17) * (8^14).
Now, to generate an expression with positive exponents only, we can rewrite (8^14) as (1/8^14).
Substituting this back into the expression, we have 1/(3^17) * (1/8^14).
Therefore, the expression equivalent to 3^-17/8^-14 with positive exponents only is 1/(3^17) * (1/8^14).
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
(7^-3)^7 * 7^20/6^2 = _
(7^-3)^7 * 7^20/6^2 = _
To generate equivalent expressions with only positive exponents, we can apply the properties of integer exponents.
First, let's evaluate (7^-3)^7. The property of exponentiation tells us that taking an exponent to another exponent is equivalent to multiplying the exponents. In this case, we multiply -3 by 7:
(7^-3)^7 = 7^(-3 * 7) = 7^-21
Next, let's simplify 7^20/6^2. The property of exponents tells us that dividing two numbers with the same base but different exponents is equivalent to subtracting the exponents. In this case, we subtract the exponents of 7 and 6:
7^20/6^2 = 7^(20-2) = 7^18
Substituting these simplified expressions back into the original expression, we have:
(7^-3)^7 * 7^20/6^2 = 7^-21 * 7^18
Now, we can apply the property of exponents that states when multiplying two numbers with the same base, we add the exponents:
7^-21 * 7^18 = 7^(-21 + 18) = 7^-3
Therefore, the expression (7^-3)^7 * 7^20/6^2 simplifies to 7^-3.
Recall that any number raised to the power of -1 gives the reciprocal of the number, so 7^-3 = 1/7^3.
The answer, as an improper fraction, is 1/343.
First, let's evaluate (7^-3)^7. The property of exponentiation tells us that taking an exponent to another exponent is equivalent to multiplying the exponents. In this case, we multiply -3 by 7:
(7^-3)^7 = 7^(-3 * 7) = 7^-21
Next, let's simplify 7^20/6^2. The property of exponents tells us that dividing two numbers with the same base but different exponents is equivalent to subtracting the exponents. In this case, we subtract the exponents of 7 and 6:
7^20/6^2 = 7^(20-2) = 7^18
Substituting these simplified expressions back into the original expression, we have:
(7^-3)^7 * 7^20/6^2 = 7^-21 * 7^18
Now, we can apply the property of exponents that states when multiplying two numbers with the same base, we add the exponents:
7^-21 * 7^18 = 7^(-21 + 18) = 7^-3
Therefore, the expression (7^-3)^7 * 7^20/6^2 simplifies to 7^-3.
Recall that any number raised to the power of -1 gives the reciprocal of the number, so 7^-3 = 1/7^3.
The answer, as an improper fraction, is 1/343.
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
The product rule of integer exponents states that when multiplying two powers with the same base, you add the exponents.
In this case, we have 12^-5 * 12^7.
To apply the product rule of integer exponents, we add the exponents together: -5 + 7 = 2.
Therefore, 12^-5 * 12^7 simplifies to 12^2.
Calculating 12^2, we multiply 12 by itself: 12 * 12 = 144.
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.
To summarize, we used the product rule of integer exponents by adding the exponents (-5 + 7) to simplify the expression to 12^2, and then calculated 12^2 to obtain the numerical value of 144.
In this case, we have 12^-5 * 12^7.
To apply the product rule of integer exponents, we add the exponents together: -5 + 7 = 2.
Therefore, 12^-5 * 12^7 simplifies to 12^2.
Calculating 12^2, we multiply 12 by itself: 12 * 12 = 144.
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.
To summarize, we used the product rule of integer exponents by adding the exponents (-5 + 7) to simplify the expression to 12^2, and then calculated 12^2 to obtain the numerical value of 144.
1 answer