Question

(1 point) The expression

where n, the leading coefficient, is:
and r, the exponent of a, is: 3
and S, the exponent of b, is: 10
and finally t, the exponent of c, is: 15
(5b¹c-5)-³(4b⁰a²)-5 equals na'bs ct
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NOTE: The value for n may be given as a fraction or as a just number. All other values must be
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Answer 1

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

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)=(1)/(5^34^5)a^(-10)b^(-3)c^(15)=\boxed{(1)/(128000)a^(-10)b^(-3)c^(15)}`

In terms of answer requirements:

n = 1/128000

r = -10

s = -3

t = 15