Question

(-25)raised to the -4 power times (5 raised to the -3 power) raised to the -2 powerI'll upload a picture

Answer 1

(-25)^4*5(^-3)^(-2)

Replace constants in factor: (-25)*4 with 390625

It becomes 390625*5(^-3)^(-2)

Look at 390625*5^-3^-2

Replace constants in factor: 5*-3*-2 with 1.1958131745004

It becomes 390625*1.1958131745004

Result: 390625*1.1958131745004

Answer 2

Hello there. To solve this question, we need to remember some properties on powers.

(-25)^(-4) * (5^(-3))^(-2)

To start, remember a^(-n) = 1/a^n, for a not equal to 0. Also, (ab)^n = a^n * b^n and (a^b)^c = a^(b*c)

Such that we have:

(-1)^(-4) * 25^(-4) * 5^((-3)*(-2))

1/(-1)^4 * (5^2)^(-4) * 5^6

Since (-1)^4 is equal to 1, we get:

5^(2*(-4)) * 5^6

5^(-8) * 5^6

Knowing that a^b * a^c = a^(b + c), we get:

5^(-8+6)

5^(-2)

Applying the first rule, we get:

1/5^2

1/25.