Question

-2m^3 n^2 to the power of 4

Answer 1

`16m^(12)n^(8)`

Explanation:

The rule of exponents for powers of powers applies.

`(a^b)^c=a^(b\cdot c)\qquad\text{the applicable rule}\\\\(-2m^(3)n^(2))^(4)=(-2)^(4)m^(3\cdot 4)n^(2\cdot 4)\\\\=16m^(12)n^(8)`

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The rules of exponents are not hard to remember if you recall that an exponent signifies repeated multiplication. That is ...

... a^3 = a·a·a . . . . . . the factor a appears 3 times in the product

so (a^3)^2 = (a·a·a)·(a·a·a) = a^(3·2) = a^6