Question

How do you simplify `(-2x^2)^3(4x^3)^-1`?

Answer 1

`-2x^3`

Explanation:

Rule #1:

`(a^b)^c = a^(b*c)`

Rule #2

`a^-1 = 1/a`

Rule #3

`(a^b)/(a^c) = a^(b-c`

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`(-2x^2)^3(4x^3)^-1`

Use rules `1` and `2` (mentioned above) of exponents

`(-2^3x^(2*3))(1/(4x^3))`

Simplify by multiplying out the exponents

`(-8x^6)(1/(4x^3))`

Write as fractions

`(-8x^6)/1 * 1/(4x^3)`

Rewrite as a single fraction

`((-8x^6)times1)/(1times(4x^3))`

Multiply numerator and denominator by `1`

`(-8x^6)/(4x^3)`

Simplify coefficients and then simplify variables using rule `3` from above

`(-2x^3)/1`

Write without a denominator

`-2x^3`