Question

Write the expression as a monomial in its standard form:

Answer 1

Answer:

1. 8 p^19

2.  -x^8

3. -2y^14

Step-by-step explanation:

1.   8p^15·(–p)^4

We can separate things inside the powers  (ab)^x = a^x * b^x

8 p^15 * (-1)^4 p^4

We can add the exponents when the bases are the same  x^a * x^b = x^(a+b)

8 p^ (15+4)

8 p^19

2.(-2x^2)^2*(-.25x^4)

We can separate things inside the powers  (ab)^x = a^x * b^x

(-2)^2  (x^2)^2  (-1/4) x^4

4 x^4  -1/4 x^4

We can add the exponents when the bases are the same  x^a * x^b = x^(a+b)

4 * -1/4  x^ (4+4)

-x^8

3.((-.5)y^4)^3*(16y^2)

   We can separate things inside the powers  (ab)^x = a^x * b^x

(-1/2) ^3 (y^4) ^3 (16) y^2

When a power is raised to a power, we multiply  x^a^b = x^(ab)

-1/8 * y^(4*3) * 16 y^2

-1/8 *16 y^12 * y^2

We can add the exponents when the bases are the same  x^a * x^b = x^(a+b)

-2 y^(12+2)

-2y^14