Question

simplify. express your answer using a
$(u^{-7})^{12}$

Explanation:

Step1: Apply power of a power rule

The power of a power rule states that \((a^m)^n = a^{m \times n}\). For the expression \((u^{-7})^{12}\), we multiply the exponents \(-7\) and \(12\).
$$(u^{-7})^{12}=u^{-7\times12}$$

Step2: Calculate the product of exponents

Calculate \(-7\times12\), which equals \(-84\). So we have:
$$u^{-84}$$

Step3: Rewrite with positive exponent (optional, but common)

Recall that \(a^{-n}=\frac{1}{a^n}\), so \(u^{-84}=\frac{1}{u^{84}}\). However, if we just need to simplify using exponents (including negative ones), \(u^{-84}\) is also a simplified form. But typically, positive exponents in the denominator are preferred.

Answer:

\(\frac{1}{u^{84}}\) (or \(u^{-84}\))