What is the missing exponent in the following equation?
h^450/ h? = h^215 (1 point)
The missing exponent is 449.
Simplify 12^87 ÷ 12^25. (1 point)
To simplify the expression 12^87 ÷ 12^25, we can subtract the exponents.
12^87 ÷ 12^25 = 12^(87-25) = 12^62
What is the value of 6.9 - 20? (1 point)
4.9
6.9
7.9
5.9
The value of 6.9 - 20 is -13.1.
Apply the Zero Power Rule to create an equivalent expression to 9. (−33)^0 + 3/2 (8 − 27^0). (2 points)
9. (-33)^0+ 3/2 (8-27^0) =???·??? + 3/2 (???-???)
When applied to any non-zero base, the zero power rule states that any nonzero number raised to the power of zero is equal to 1. Therefore, (-33)^0 simplifies to 1.
Using this information, the expression becomes:
1 + 3/2 (8 - 1)
Simplifying further:
1 + 3/2 (7)
Multiplying:
1 + 21/2
Combining:
2/2 + 21/2 = 23/2
Therefore, the equivalent expression to 9. (-33)^0+ 3/2 (8-27^0) is 23/2.
9. (-33)^0+ 3/2 (8-27^0) = blnack · blanck + 3/2 (blanck - blanck)
Apologies for the confusion in my previous response. Let's simplify the expression correctly.
According to the zero power rule, any non-zero number raised to the power of zero is equal to 1. So, (-33)^0 simplifies to 1.
Now, we can rewrite the expression:
1 + 3/2 (8 - 1)
Simplifying inside the parentheses:
1 + 3/2 (7)
Multiplying:
1 + 21/2
Adding:
2/2 + 21/2 = 23/2
Therefore, the simplified expression is:
9. (-33)^0 + 3/2 (8 - 27^0) = 23/2.
i need the whole equation
Apologies for the confusion. Here is the whole equation:
9. (-33)^0 + 3/2 (8 - 27^0) = 1 + 3/2 (8 - 1) = 1 + 3/2 (7) = 1 + 21/2 = 2/2 + 21/2 = 23/2.
I eed you to apply yhe power of zero to this equation 9. (-33)^0+ 3/2 (8-27^0)
Apologies for the confusion in my previous responses. Let's apply the power of zero correctly.
According to the zero power rule, any non-zero number raised to the power of zero is equal to 1. So, (-33)^0 simplifies to 1.
Now, we can rewrite the equation:
9. (-33)^0 + 3/2 (8 - 27^0) = 9(1) + 3/2 (8 - 1)
Simplifying the expression further:
= 9 + 3/2 (7)
= 9 + 21/2
Adding:
= 18/2 + 21/2
= 39/2
Therefore, the simplified expression is:
9. (-33)^0 + 3/2 (8 - 27^0) = 39/2.
Solve the expression 15.8^0 5 +4 (7^0 – 6). (1 point)
15.8^0/5 + 4 (7^0 − 6) = ?
To solve the expression 15.8^0/5 + 4 (7^0 − 6), we need to follow the order of operations (parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right).
First, we solve the exponent 15.8^0, which is equal to 1, as any number raised to the power of 0 is 1.
Next, we simplify the expression within parentheses, which is 7^0 - 6. Again, any number raised to the power of 0 is 1, so 7^0 is equal to 1. Thus, the expression becomes 1 - 6, which equals -5.
Now, we can substitute the simplified values into the original expression:
15.8^0/5 + 4(-5)
Since 15.8^0 is equal to 1, the expression becomes:
1/5 + 4(-5)
Now, we solve the multiplications:
1/5 - 20
To combine fractions, the denominators must be the same. We can rewrite 20 as 20/1:
1/5 - 20/1
To subtract fractions, we need the same denominator. To make the denominators the same, we multiply 1/5 by 1/1:
1/5 * 1/1 - 20/1
Now we have the same denominator:
1/5 - 20/1
To subtract these fractions, we need the same denominator. We can convert 1 to have the same denominator as 5:
1 = 5/5
5/5/5 - 20/1
1/5 - 20/1
Now, we have the same denominators and can subtract directly:
1/5 - 20/1 = -99/5
Therefore, the solution to the expression 15.8^0/5 + 4(7^0 − 6) is -99/5.
Use the Power Rule of Exponents to simplify (10^3)^6. (1 point)
The Power Rule of Exponents states that when raising an exponent to another power, you multiply the exponents.
In this case, we have (10^3)^6. To simplify, we multiply the exponents:
(10^3)^6 = 10^(3*6) = 10^18
Therefore, (10^3)^6 is equal to 10^18.
If the expression 715 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?
(7.7.7). (7.7 · 7) · (7 · 7 · 7) · (7 · 7 · 7) · (7 · 7 · 7)
(7-7-7-7-7)^10
(7^18)^ 3
(7^10)^ 5
If the expression 715 was 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)
Therefore, the correct option is:
(7.7.7). (7.7 · 7) · (7 · 7 · 7) · (7 · 7 · 7) · (7 · 7 · 7)
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9. (1 point)
To create a simplified equivalent expression for (19^4)^9 using the Power Rule of Exponents, we need to multiply the exponents.
(19^4)^9 = 19^(4*9) = 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)
7^-3 = ?
The Property of Negative Integer Exponents states that when a base is raised to a negative exponent, it is equal to the reciprocal of the base raised to the positive exponent.
Therefore, for 7^-3, we have:
7^-3 = 1/(7^3)
To further simplify, we can calculate 7^3, which is equal to 343.
So, the final answer is:
7^-3 = 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)
3^-17/8^-14 = ?
To apply the Property of Negative Integer Exponents, we can rewrite 3^-17/8^-14 with positive exponents.
The Property of Negative Integer Exponents states that when a term with a negative exponent is moved to the denominator, the exponent becomes positive. Similarly, when a term with a negative exponent is moved to the numerator, the exponent becomes positive.
So, we can rewrite our given expression as:
3^-17/8^-14 = 8^14/3^17
Therefore, the expression equivalent 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.
(7^-3)^7.7^20/6^-2 = ?
To apply the Properties of Integer Exponents, we need to simplify (7^-3)^7.7^20/6^-2 using positive exponents.
First, let's simplify the exponent expression:
(7^-3)^7.7^20/6^-2
Applying the Property of Negative Integer Exponents to (7^-3)^7, we have:
(7^-3)^7 = 7^(-3*7) = 7^-21
Next, applying the Property of Negative Integer Exponents to 6^-2, we get:
6^-2 = 1/6^2 = 1/36
Now, we can substitute the simplified expressions into the original expression:
(7^-3)^7.7^20/6^-2 = 7^-21 * 7^20 / 1/36
To simplify further, we can combine the terms with the same base:
7^-21 * 7^20 = 7^(20-21) = 7^-1 = 1/7^1 = 1/7
Therefore, the expression simplifies to:
1/7 / 1/36 = 1/7 * 36/1 = 36/7
The answer, as an improper fraction, is 36/7.
Simplify the expression (4x^3)^2 using the properties of integer exponents. (1 point)
8x^6
16x^5
16x^6
4x^6
To simplify the expression (4x^3)^2 using the properties of integer exponents, we multiply the exponent of 4x^3 by 2.
(4x^3)^2 = 4^2 * (x^3)^2 = 16 * x^(3*2) = 16 * x^6.
Therefore, the simplified expression is 16x^6.
Apply the properties of integer exponents to generate an equivalent algebraic expression to (4x^4y^−4)^3 (x^7y^3)^2 (1 point)
64 /x^2y^18
x^2y^18/ 64
64/ x^20
4/x^2y^18
To generate an equivalent algebraic expression to (4x^4y^−4)^3 (x^7y^3)^2 using the properties of integer exponents, we need to simplify each term separately and then multiply them together.
Let's start with (4x^4y^−4)^3:
(4x^4y^−4)^3 = 4^3 * (x^4)^3 * (y^−4)^3 = 64 * x^(4*3) * y^(−4*3) = 64 * x^12 * y^(−12)
Next, let's simplify (x^7y^3)^2:
(x^7y^3)^2 = (x^7)^2 * (y^3)^2 = x^(7*2) * y^(3*2) = x^14 * y^6
Now, we multiply the two simplified terms together:
(64 * x^12 * y^(−12)) * (x^14 * y^6) = 64 * x^12 * x^14 * y^(−12) * y^6 = 64 * x^(12+14) * y^(−12+6) = 64 * x^26 * y^(−6)
Therefore, an equivalent algebraic expression to (4x^4y^−4)^3 (x^7y^3)^2 is 64 * x^26 * y^(−6).
Whats the answer?
The answer is 64 * x^26 * y^(-6).
These are the choices
64 /x^2y^18
x^2y^18/ 64
64/ x^20
4/x^2y^18
Apologies for the confusion. Among the given choices, the answer is:
64 / x^2y^18.
Apply the product rule of integer exponents to find the numerical equivalent of 12-5. 127. Show your work and explain how you used the product rule of integer exponents. (2 points)
To find the numerical equivalent of 12^(-5) * 1^27, we can use the product rule of integer exponents, which states that the product of two numbers with the same base can be simplified by adding their exponents.
First, let's evaluate 12^(-5). According to the product rule of integer exponents, since the base is the same (12), we can add the exponents:
12^(-5) = 1/(12^5)
Now, let's simplify 1^27. According to the product rule of integer exponents, any number raised to the power of 1 is itself. Therefore, 1^27 is equal to 1.
Now, we can substitute the simplified expressions back into the original expression:
12^(-5) * 1^27 = 1/(12^5) * 1
Multiplying the fractions:
1 * 1 = 1
Therefore, the numerical equivalent of 12^(-5) * 1^27 is 1.