Questions: (-3w^3x^-4)^3

Solution Steps

To simplify the expression \(\left(-3 w^{3} x^{-4}\right)^{3}\) and write it using only positive exponents, we need to apply the power of a power rule \((a^m)^n = a^{m \cdot n}\) to each term inside the parentheses. This will involve raising \(-3\), \(w^3\), and \(x^{-4}\) to the power of 3.

Given the expression \(\left(-3 w^{3} x^{-4}\right)^{3}\), we need to apply the power rule \((a^m)^n = a^{m \cdot n}\) to each term inside the parentheses.

Raise the coefficient \(-3\) to the power of 3: \[ (-3)^3 = -27 \]

Raise the exponent of \(w\) to the power of 3: \[ (w^3)^3 = w^{3 \cdot 3} = w^9 \]

Raise the exponent of \(x\) to the power of 3: \[ (x^{-4})^3 = x^{-4 \cdot 3} = x^{-12} \]

Convert the negative exponent of \(x\) to a positive exponent: \[ x^{-12} = \frac{1}{x^{12}} \]

Final Answer