Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x3y−412x7y4.(1 point)

Question

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

14x4y8

Answer 1

None of the given responses are correct.

To generate an equivalent algebraic expression to 3x^3y − 4^12x^7y^4, we can apply the properties of integer exponents.

Using the product rule, the coefficients can be multiplied together: 3 * (-4^12) = -12^12.

Then, using the power rule, the variables with the same base can be combined by adding their exponents: x^3 * x^7 = x^10 and y * y^4 = y^5.

Putting it all together, the equivalent algebraic expression is:

-12^12x^10y^5.

Answer 2

Apply the properties of integer exponents to simplify the algebraic expression (2xy3)4⋅(x2y)3.(1 point)
Responses

32x10y11
32 x superscript 10 baseline y superscript 11 baseline

16x25
16 x superscript 25 baseline

x10y15
x superscript 10 baseline y superscript 15 baseline

16x10y15

Answer 3

To simplify the algebraic expression (2xy^3)^4 ⋅ (x^2y)^3, we can apply the properties of integer exponents.

First, apply the exponent outside the parentheses to each term inside the parentheses: (2^4)(x^4)(y^12) ⋅ (x^6)(y^3).

Next, multiply the coefficients: 2^4 = 16 and x^4 * x^6 = x^(4 + 6) = x^10.

Finally, combine like terms by adding the exponents of y: y^12 * y^3 = y^(12 + 3) = y^15.

Putting it all together, the simplified algebraic expression is:

16x^10y^15.

Answer 4

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

9c1025a14b8
Start Fraction 9 c superscript 10 baseline over 25 a superscript 14 baseline b superscript 8 baseline End Fraction

−5c103a14b8

Answer 5

To simplify the algebraic expression (-5a^3b^4c^-2/3a^-4b^0c^3)^-2, we can apply the properties of integer exponents.

First, apply the negative exponent rule to rewrite the expression as (1/(-5a^3b^4c^-2/3a^-4b^0c^3))^2.

Next, apply the exponent to each term inside the parentheses: (1/(-5)^2(a^3)^2(b^4)^2(c^-2/3)^2(a^-4)^2(b^0)^2(c^3)^2).

Simplify each term: (1/25a^6b^8c^-4/3a^-8b^0c^6).

Apply the properties of exponents to combine like terms: (c^-4/3c^6) * (a^6/a^-8) * (b^8/b^0).

Simplify each term: (c^(6 - 4/3)) * (a^(6 - (-8))) * (b^(8 - 0)).

Simplify the exponents: c^(6/3) * a^14 * b^8.

Simplify further: c^2 * a^14 * b^8.

The simplified algebraic expression is: c^2a^14b^8.