Use the properties of integer exponents to simplify the expression (−4a^4)(−2a^2).(1 point)
Responses
−8a6
negative 8 a superscript 6 baseline
8a8
8 a superscript 8 baseline
8a6
8 a superscript 6 baseline
8a^2
To simplify the expression (−4a^4)(−2a^2), we can multiply the coefficients and add the exponents.
The coefficient is -4 * -2 = 8
The variable "a" has exponents of 4 and 2, so we add them: 4 + 2 = 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
4x4y8
4 x superscript 4 baseline y superscript 8 baseline
312x4y8
Start Fraction 3 over 12 x superscript 4 baseline y superscript 8 baseline
14x12
Start Fraction 1 over 4 x superscript 12 baseline
1/4x^4y^8
To generate an equivalent algebraic expression to 3x^3y^−4/12x^7y^4, we can apply the properties of integer exponents:
First, let's simplify the coefficients: 3/12 = 1/4.
Then, for the variable "x," we subtract the exponents: 3 - 7 = -4.
For the variable "y," we subtract the exponents: -4 + 4 = 0.
Simplifying 3x^3y^-4/12x^7y^4 using the properties of integer exponents gives us 1/4x^(-4)y^0.
Since any number with an exponent of 0 is equal to 1, we can simplify further to give:
1/4x^(-4)y^0 = 1/4x^(-4) = 1/(4x^4).
Therefore, the equivalent algebraic expression is 1/(4x^4).
thats not one of the answers
Apologies for the confusion. Let's go through the options again:
- The option "4x4y8" is not correct. It does not account for the given exponents and does not simplify the expression correctly.
- The option "312x4y8" is also not correct. It does not simplify the expression correctly.
- The option "14x12" is not correct either. It does not simplify the expression correctly.
- The correct equivalent algebraic expression is "1/4x^4y^8."
Again, apologies for any confusion caused.
Apply the properties of integer exponents to simplify the algebraic expression (2xy3)4⋅(x2y)3.(1 point)
Responses
16x25
16 x superscript 25 baseline
16x10y15
16 x superscript 10 baseline y superscript 15 baseline
32x10y11
32 x superscript 10 baseline y superscript 11 baseline
x^10 y^15
To simplify the algebraic expression (2xy^3)^4⋅(x^2y)^3, we will apply the properties of integer exponents:
First, let's simplify the exponent of the first factor: (2xy^3)^4 = 2^4 * x^4 * (y^3)^4 = 16x^4y^12.
Next, let's simplify the exponent of the second factor: (x^2y)^3 = (x^2)^3 * y^3 = x^6y^3.
Now, we can multiply the simplified factors together: (16x^4y^12) * (x^6y^3) = 16x^4 * x^6 * y^12 * y^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 (−5a3b4c−23a−4b0c3)−2.(1 point)
Responses
c10a14b8
Start Fraction c superscript 10 baseline over a superscript 14 baseline b superscript 8 baseline End Fraction
925a12
Start Fraction 9 over 25 a superscript 12 baseline End Fraction
−5c103a14b8
Start Fraction negative 5 c superscript 10 baseline over 3 a superscript 14 baseline b superscript 8 baseline End Fraction
9c^10/25a^14b^8
To simplify the algebraic expression (−5a^3b^4c^−2)(−3a^−4b^0c^3)−2, we will apply the properties of integer exponents:
First, let's simplify the exponents within the first factor:
(−5a^3b^4c^−2)^−2 = (-5)^-2 * (a^3)^-2 * (b^4)^-2 * (c^-2)^-2
= 1/(-5)^2 * 1/(a^3)^2 * 1/(b^4)^2 * 1/(c^-2)^2
= 1/25 * 1/a^6 * 1/b^8 * 1/c^-4
= 1/25a^6b^8c^-4
Now, let's simplify the exponents within the second factor:
(−3a^-4b^0c^3)^-2 = (-3)^-2 * (a^-4)^-2 * (b^0)^-2 * (c^3)^-2
= 1/(-3)^2 * 1/(a^-4)^2 * 1/(b^0)^2 * 1/(c^3)^2
= 1/9 * 1/a^-8 * 1/1 * 1/c^6
= 1/9a^-8c^6
Now, let's multiply the simplified factors together:
(1/25a^6b^8c^-4)(1/9a^-8c^6) = 1/(25*9*a^6*a^-8*b^8*c^-4*c^6)
= 1/(225*a^(6-8)*b^8*c^(-4+6))
= 1/(225*a^-2*b^8*c^2)
= 1/(225*c^2/a^2*b^8)
= a^2b^-8c^-2/225
Therefore, the simplified algebraic expression is a^2b^-8c^-2/225, or in alternate form: 1/(225a^2b^8c^2).