Question

(1 point) The expression

Answer 1

Answer:

• n = 1/128000
• r = -10
• s = -3
• t = 15

Step-by-step explanation:

You want the simplified form of (5b^1c^-5)^-3(4b^0a^2)^-5.

Rules of exponents

There are several useful rules of exponents here:

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  a^-b = 1/(a^b)

Application

Simplifying the top-level exponents first, we have ...

  $(5b^1c^{-5})^{-3}(4b^0a^2)^{-5}=(5^{-3}b^{1(-3)}c^{(-5)(-3)})(4^{-5}b^{0(-5)}a^{2(-5)})\\\\=(5^{-3}4^{-5})a^{-10}b^{-3+0}c^{15}=\dfrac{1}{5^34^5}a^{-10}b^{-3}c^{15}=\boxed{\dfrac{1}{128000}a^{-10}b^{-3}c^{15}}$

In terms of answer requirements:

  n = 1/128000

  r = -10

  s = -3

  t = 15