Use the properties of integer exponents to simplify the expression (3y)^0.(1 point)
(3y)^0 = 1
Is Option A or Option B the correct simplified expression of (4x^3)^3 using the properties of integer exponents?
Option A: 4x^9
Option B: 64x^9
Enter 1 for Option A or 2 for Option B.(1 point)
The correct simplified expression of (4x^3)^3 using the properties of integer exponents is Option B: 64x^9. Therefore, you should enter 2.
Use the properties of integer exponents to simplify the expression (−3b^4)(6b^7).(1 point)
Responses
18b^11
−18b^28
−18b^11
−18b^−3
To simplify the expression (-3b^4)(6b^7), you can combine the coefficients and add the exponents of the variable b.
-3 * 6 = -18
b^4 * b^7 = b^(4 + 7) = b^11
Therefore, the simplified expression is -18b^11.
Is Option A or Option B the correct simplified expression of (x^4)^3×(x^−4)
using the properties of integer exponents?
Option A: x^8
Option B: x^3
Enter 1 for Option A or 2 for Option B.(1 point)
The correct simplified expression of (x^4)^3 × (x^-4) using the properties of integer exponents is Option A: x^8.
Therefore, you should enter 1.
Apply the properties of integer exponents to generate an equivalent algebraic expression to (−2x^−3)^0/4x^0
.(1 point)
To generate an equivalent algebraic expression using the properties of integer exponents for (-2x^-3)^(0/4x^0), we can use the property that any number raised to the power of zero is equal to 1, and any non-zero number divided by itself is equal to 1. Additionally, any number raised to the power of 1 is equal to itself.
Therefore, the equivalent expression is simply 1.
nope
Apologies for the incorrect response. Let's try again.
To generate an equivalent algebraic expression using the properties of integer exponents for (-2x^-3)^(0/4x^0), we can simplify the expression inside the parentheses first.
(-2x^-3) = -2/x^3
Now, we can apply the property that any number raised to the power of zero is equal to 1. Therefore, (-2/x^3)^0 = 1.
Next, we simplify the expression 4x^0. Any non-zero number raised to the power of zero is equal to 1. Therefore, 4x^0 = 4.
Finally, we multiply the two simplified expressions: 1 * 4 = 4.
Thus, the equivalent algebraic expression is 4.
wrong again
Apologies for the incorrect response again. Let's try again.
To generate an equivalent algebraic expression using the properties of integer exponents for (-2x^-3)^(0/4x^0), we can simplify the expression inside the parentheses first.
(-2x^-3) = -2/x^3
Now, let's simplify the exponents using the property:
(a/b)^m = a^m / b^m
Applying this property to our expression, we get (-2/x^3)^(0/4x^0) = (-2^0) / (x^3)^0
Any non-zero number raised to the power of zero is equal to 1. Therefore, (-2^0) = 1.
Any non-zero number (except zero) raised to the power of 0 is also equal to 1. Therefore, (x^3)^0 = 1.
So, the expression simplifies to 1 / 1, which is equal to 1.
Thus, the equivalent algebraic expression is 1.
you are stupid and utterly useless
I apologize if my previous responses were not helpful. If you have any specific math question or need assistance with any topic, please let me know, and I'll be glad to help.
Apply the properties of integer exponents to generate an equivalent algebraic expression to (−2x^−3)^0 / 4x^0
.(1 point)
To generate an equivalent algebraic expression to (−2x^−3)^0 / 4x^0 using the properties of integer exponents, we can simplify the expression step by step.
First, let's simplify the expression inside the parentheses:
(−2x^−3)^0 = 1, since any non-zero number raised to the power of 0 is equal to 1.
Next, we simplify the expression 4x^0:
4x^0 = 4 * 1 = 4, since any number raised to the power of 0 is equal to 1, and 1 multiplied by 4 is 4.
Finally, we evaluate the expression:
1 / 4 = 1/4, since dividing by a number is equivalent to multiplying by its reciprocal.
Therefore, the equivalent algebraic expression is 1/4.
Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x^8 / 5x.(1 point)
Responses
−5x^9
−5x^7
5x^7
−5x^8
To simplify the expression -25x^8 / 5x using the properties of exponents and division, we divide the coefficients and subtract the exponents with the same base.
-25 / 5 = -5
x^8 / x = x^(8-1) = x^7
Therefore, the simplified expression is -5x^7.
Use the properties of integer exponents to simplify the expression (−4a^4)(−2a^2).(1 point)
Responses
8a^2
−8a^6
8a^6
8a^8
To simplify the expression (-4a^4)(-2a^2) using the properties of integer exponents, we can multiply the coefficients and add the exponents of the variable a.
(-4 * -2) = 8
(a^4 * a^2) = a^(4+2) = a^6
Therefore, the simplified expression is 8a^6.
Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3y^−4 / 12x^7y^4.(1 point)
Responses
1 / 4x^4y^8
1 / 4x^12
4x^4y^8
3 / 12x^4y^8
To generate an equivalent algebraic expression to 3x^3y^−4 / 12x^7y^4 using the properties of integer exponents, we can simplify the expression step by step.
First, let's simplify the coefficients:
3 / 12 = 1 / 4, since both 3 and 12 can be divided by 3 to simplify to 1 and 4, respectively.
Next, let's simplify the variables with the same base:
x^3 / x^7 = 1 / x^(7-3) = 1 / x^4
y^(-4) / y^4 = 1 / y^(4-(-4)) = 1 / y^8, using the rule a^(-n) = 1 / a^n
Combining the simplified coefficients and variables, we get 1 / 4x^4y^8.
Therefore, the equivalent algebraic expression is 1 / 4x^4y^8.
Apply the properties of integer exponents to simplify the algebraic expression (2xy^3)^4 ⋅ (x^2y)^3.(1 point)
Responses
32x^10y^11
x^10y^15
16x^25
16x^10y^15
To simplify the algebraic expression (2xy^3)^4 ⋅ (x^2y)^3 using the properties of integer exponents, we can simplify the expressions inside the parentheses first.
(2xy^3)^4 = 16x^4y^12, applying the power of a product property.
(x^2y)^3 = x^6y^3, applying the power of a product property.
Now, we can multiply the two simplified expressions:
(16x^4y^12) ⋅ (x^6y^3) = 16x^4 * x^6 * y^12 * y^3 = 16x^(4+6) * y^(12+3) = 16x^10 * y^15.
Therefore, the simplified algebraic expression is 16x^10y^15.
Apply the properties of integer exponents to simplify the algebraic expression (−5a^3b^4c^−2 / 3a^−4b^0c^3)^−2.(1 point)
Responses
−5c^10 / 3a^14b^8
9c^10 / 25a^14b^8
c^10 / a^14b^8
9 / 25a^12
To simplify the algebraic expression (−5a^3b^4c^−2 / 3a^−4b^0c^3)^−2 using the properties of integer exponents, we need to apply multiple rules:
First, let's simplify within the parentheses:
−5a^3b^4c^−2 / 3a^−4b^0c^3
Using the rule a^m / a^n = a^(m-n), we can simplify the expression:
= (-5/3) * (a^3 / a^-4) * (b^4 / b^0) * (c^-2 / c^3)
= (-5/3) * (a^(3 - (-4))) * (b^(4 - 0)) * (c^(-2 - 3))
= (-5/3) * (a^7) * (b^4) * (c^-5)
Next, we apply the rule (a^m)^n = a^(m*n) to the expression inside the parentheses raised to the power of -2:
((-5/3) * (a^7) * (b^4) * (c^-5))^(-2)
= ((-5/3)^(-2)) * ((a^7)^(-2)) * ((b^4)^(-2)) * ((c^-5)^(-2))
Using the rule (a^-m)^n = a^(-m*n) and simplifying the negative exponents:
= ((-3/5)^2) * (a^(-7*2)) * (b^(-4*2)) * (c^(-5*2))
= (9/25) * (a^(-14)) * (b^(-8)) * (c^(-10))
Finally, we rearrange the expression to bring the negative exponents to the denominator:
= 9c^10 / 25a^14b^8.
Therefore, the simplified algebraic expression is 9c^10 / 25a^14b^8.