What is the missing exponent in the following equation?
h^450/h^? = h^215(1 point)
The missing exponent in the equation is 235.
Simplify 12^87 ÷ 12^25
To simplify this expression, you can subtract the exponents while keeping the same base:
12^87 ÷ 12^25 = 12^(87-25) = 12^62
What is the value of 6.9−2^0?(1 point)
Responses
6.9
6.9
4.9
4.9
5.9
5.9
7.9
The value of 6.9 - 2^0 is 6.9.
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(
–
)
Applying the Zero Power Rule, any nonzero number raised to the power of 0 is equal to 1. Therefore, (-33)^0 is equal to 1.
By substituting the value, the expression becomes:
9 * 1 + 3/2(8 - 1)
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0).(2 points)
Applying the Zero Power Rule, any nonzero number raised to the power of 0 is equal to 1. Therefore, (-33)^0 is equal to 1.
By substituting the value, the expression becomes:
9 * 1 + 3/2(8 - 1) = 9 + 3/2(7)
Solve the expression 15⋅8^0/5+4(7^0−6).(1 point)
To solve the expression, let's follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Given expression: 15⋅8^0/5+4(7^0−6)
First, we simplify the exponent:
7^0 is equal to 1.
Now, we can simplify the parentheses:
(7^0 - 6) = (1 - 6) = -5
Next, we perform the multiplication and division from left to right:
15 * 8^0 / 5 = 15 * 1 / 5 = 15 / 5 = 3
Finally, we perform the addition and subtraction from left to right:
3 + 4(-5) = 3 + (-20) = -17
Therefore, the solution to the expression is -17.
Use the Power Rule of Exponents to simplify (10^3)^6.(1 point)
Using the Power Rule of Exponents, we can simplify (10^3)^6 by multiplying the exponents:
(10^3)^6 = 10^(3 * 6) = 10^18
Therefore, (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
(7^10)^5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline
(7^18)^3
left parenthesis 7 superscript 18 baseline right parenthesis cubed
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis
(7⋅7⋅7⋅7⋅7)10
If the expression 7^15 was simplified using the Power Rule of Exponents, the correct expanded equivalent expression would be:
(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)
This can also be written as:
(7^5)^5
Therefore, the correct option is:
(left parenthesis 7 superscript 5 baseline right parenthesis superscript 5 baseline)
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 (19^4)^9 by multiplying the exponents:
(19^4)^9 = 19^(4 * 9) = 19^36
Therefore, a 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)
Applying the Property of Negative Integer Exponents, we can rewrite 7^(-3) as the reciprocal of 7^3:
7^(-3) = 1 / 7^3
Therefore, the solution for 7^(-3) without any exponent expression or decimals is 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)
Applying the Property of Negative Integer Exponents, we can rewrite 3^(-17)/8^(-14) with positive exponents only:
3^(-17) / 8^(-14) = 1 / (3^17 * 1/8^14)
Since 1/8^14 is equal to 8^(-14) by taking the reciprocal, we can further simplify:
1 / (3^17 * 1/8^14) = 1 / (3^17 * 8^(-14))
By applying the Product Rule of Exponents to combine the bases:
1 / (3^17 * 8^(-14)) = 1 / (2^14 * 3^17)
Therefore, an expression equivalent to 3^(-17)/8^(-14) with positive exponents only is 1 / (2^14 * 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 generate equivalent expressions with only positive exponents, we'll first apply the Property of Integer Exponents to simplify (7^-3)^7:
(7^-3)^7 = 7^(-3 * 7) = 7^-21
Next, we'll apply the Property of Integer Exponents to simplify the expression 7^20/6^-2:
7^20/6^-2 = 7^20 * 6^2
Combining the two expressions, we have:
(7^-3)^7 ⋅ 7^20/6^-2 = 7^-21 ⋅ 7^20 * 6^2
Now, using the Property of Exponents, we can simplify the expression further:
7^-21 ⋅ 7^20 * 6^2 = 7^(-21 + 20) * 6^2 = 7^-1 * 6^2
Since 7^-1 is equal to the reciprocal of 7^1, we have:
7^-1 * 6^2 = 1/7^1 * 6^2 = 1/7 * 6^2
Finally, simplifying the expression:
1/7 * 6^2 = 1/7 * 36 = 36/7
Therefore, the solution to the expression is 36/7 as an improper fraction.
Simplify the expression (4x^3^)2 using the properties of integer exponents.(1 point)
Responses
8x^6
8 x superscript 6 baseline
16x^5
16 x superscript 5 baseline
16x^6
16 x superscript 6 baseline
4x^6
To simplify the expression (4x^3)^2 using the properties of integer exponents, we need to apply the power to each term inside the parentheses.
(4x^3)^2 = 4^2 * (x^3)^2
Squaring 4 results in 16:
4^2 = 16
Squaring x^3 results in x^6:
(x^3)^2 = x^(3 * 2) = x^6
Now, combining the simplified terms:
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)
Responses
x2y1864
Start Fraction x squared y superscript 18 baseline over 64 End Fraction
64x20
Start Fraction 64 over x superscript 20 baseline End Fraction
4x2y18
Start Fraction 4 over x squared y superscript 18 baseline End Fraction
64x2y18
Start Fraction 64 over x squared y superscript 18 baseline End Fraction
To generate an equivalent algebraic expression to (4x^4y^(-4))^3/(x^7y^3)^2 using the properties of integer exponents, we can simplify each term separately.
First, let's simplify (4x^4y^(-4))^3:
(4x^4y^(-4))^3 = 4^3 * (x^4)^3 * (y^(-4))^3
Simplifying the powers within the parentheses:
4^3 = 64
(x^4)^3 = x^(4 * 3) = x^12
(y^(-4))^3 = y^(-4 * 3) = y^(-12)
So, (4x^4y^(-4))^3 becomes:
64x^12y^(-12)
Next, let's simplify (x^7y^3)^2:
(x^7y^3)^2 = (x^7)^2 * (y^3)^2
Simplifying the powers within the parentheses:
(x^7)^2 = x^(7 * 2) = x^14
(y^3)^2 = y^(3 * 2) = y^6
So, (x^7y^3)^2 becomes:
x^14y^6
Now, we can rewrite the expression using the simplified terms:
(4x^4y^(-4))^3/(x^7y^3)^2 = (64x^12y^(-12))/(x^14y^6)
To simplify this further, we subtract the exponents of like bases in the numerator and denominator:
64x^12y^(-12) / x^14y^6 = 64x^(12 - 14) * y^(-12 - 6) = 64x^(-2) * y^(-18)
Finally, we can rewrite the expression with positive exponents:
64 / (x^2 * y^18)
Therefore, the equivalent algebraic expression is 64 / (x^2 * y^18).
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
The product rule of integer exponents states that when you have two expressions with the same base being multiplied, you can add their exponents.
To find the numerical equivalent of 12^(-5)⋅12^7, we can use the product rule of integer exponents:
12^(-5)⋅12^7 = 12^(-5+7) = 12^2
Now, we can calculate 12^2:
12^2 = 12 * 12 = 144
Therefore, the numerical equivalent of 12^(-5)⋅12^7 is 144.