A technician is using a formula that contains the algebraic expression $(6k^3)^{-2}$. Which of the following represents the correct first step to simplify this expression?

An engineering student is simplifying a formula for material stress that includes the expression $(6k^3)^{-2}$. To reach the final form of $\frac{1}{36k^6}$, they must apply several exponent properties in sequence. Match each property name to the specific mathematical step it justifies in this process.

An engineering assistant is simplifying the formula $(2b^3)^{-4}$ for a technical report. Arrange the following steps in the correct order to simplify the expression using positive exponents, according to the standard properties of exponents.

A solar energy technician is using a calibration formula that includes the expression $(2b^3)^{-4}$. After simplifying the expression using exponent properties and writing it with only positive exponents, the numerical coefficient in the denominator is ____.

A trainee is reviewing a technical manual and sees the expression $(6k^3)^{-2}$ used to calculate wire resistance. When applying exponent properties to begin simplifying this expression, the exponent $-2$ is only applied to the variable $k^3$, resulting in the expression ${}6(k^3)^{-2}$.

Documenting Steps for Algebraic Simplification

Recalling Exponent Properties for Quality Control Calculations