Question

Simplify the following monomials (-a²b)ª

Answer 1

`\displaystyle{(-1)^aa^(2a) b^a}`

Explanation:

The following expression can be rewritten as:

`\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a}`

In this case, we have to separate -1 out of a² since if a becomes even, the value of (-a)ª will become positive while (-a)ª becomes negative when a is odd.

We can apply the law of exponent when:

`\displaystyle{\left(a \cdot b \cdot c \right)^m = a^m \cdot b^m \cdot c^m}`

Therefore:

`\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^a\cdot a^(2a)\cdot b^a}\\\\\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^aa^(2a) b^a}`

This will make when a = even numbers, the expression is positive while negative when a is odd.

And no, the answer is not
`-a^(2a) b^a` since this will make the expression negative only but the problem can be positive when a = even number which is why we have to separate -1 out of -a² so that it meets the condition.

Hence, the answer is
`\displaystyle{(-1)^aa^(2a) b^a}`