Question

Solve and simplify contains only positive exponents

Answer 1

-27m⁶n¹²

Explanation:

You want the simplified form of (-3m²n⁴)³.

Rules of exponents

The applicable rules of exponents are ...

(ab)^c = (a^c)(b^c)

(a^b)^c = a^(bc)

Application

`(-3m^2n^4)^3=(-3)^3(m^2)^3(n^4)^3=-27m^(2\cdot3)n^(4\cdot3)\\\\=\boxed{-27m^6n^(12)}`

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Additional comment

It can be helpful to think of an exponent as signifying repeated multiplication, in much the same way that a coefficient signifies repeated addition.

(-3)³ = (-3)(-3)(-3) . . . . the factor is repeated 3 times

= 9(-3) = -27