Write the expression as a monomial in its standard form:

1. (-2x^2) ^2 * (-.25x^4)

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

1.-x^8

2. - 2y^14

Step-by-step explanation:

1. (-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

2. ((-.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