Question

Solve and simplify this expression.

Answer 1

\[\left(- \frac{ 2 }{ 3 } \right)^{-4}\]

Answer 2

this isn't an equation. It's an expression. It's your job to evaluate the expression.

1. Since you have -4 as exponent here, you can invert the -2/3, keeping the parentheses, and using the new exponent +4.

Try this, please.

Answer 3

If you had \(a^{-1}\) what would than mean?

Answer 4

The first rule:
\(\color{#000000}{ \displaystyle ~[1]\quad \quad \left(a\times b\right)^{x} = \left(a\right)^{x} \times \left(b\right)^{x} }\)

This is true for any amount of numbers. That is,
\(\color{#000000}{ \displaystyle ~\left(a\times b\times \dots \times c\right)^{x} =\left(a\right)^{x} \times \left(b\right)^{x}\times \dots \times \left(c\right)^{x} }\)
\(\color{blue}{\text{----------------------------------------------------------}}\)

The second rule:
\(\color{#000000}{ \displaystyle ~[2]\quad \quad a^{-x} = \frac{1}{a^x} }\)
\(\color{blue}{\text{----------------------------------------------------------}}\)

The third rule: (It's a consequence of [1] and [2])
\(\color{#000000}{ \displaystyle ~[2]\quad \quad \left(\frac{a}{c}\right)^{-x} = \left(\frac{c}{a}\right)^{x} }\)
\(\color{blue}{\text{----------------------------------------------------------}}\)

The forth rule:
\(\color{#000000}{ \displaystyle ~[3]\quad \quad \left(-1\right)^{x} = -1 }\) when \(\color{#000000}{ \displaystyle x }\) is odd
\(\color{#000000}{ \displaystyle ~~~~~\quad \quad \left(-1\right)^{x} = 1 }\) when \(\color{#000000}{ \displaystyle x }\) is even
\(\color{blue}{\text{----------------------------------------------------------}}\)