Question

PLS HELP ME QUICK!! PROVIDE AN EXPLANATION PLS

Answer 1

The first option,
`(3^6)/(6^(15))`.

Explanation:

Using the rules of exponents to solve the given question.

`\boxed{\left\begin{array}{ccc}\text{\underline{Exponent rules:}}\\1.\ a^0=1\\2.\ a^m * a^n=a^(m+n)\\3.\ a^m / a^n=a^(m-n)\\4.\ (ab)^m=a^mb^m\\5.\ (a/b)^m=a^m/b^m\\6.\ (a^m)^n=a^(mn)\\7.\ a^(-m)=1/a^m\\8.\ a^(m/n)=(\sqrt[n]{a} )^m\end{array}\right}`

Given:

`((6^(-3))/(3^(-2)*6^2) )^3\\\\\text{Use rule 7 on the numerator term} \Longrightarrow ((1)/(3^(-2)*6^2*6^(3)) )^3\\\\\text{Use rule 2 on the denominator} \Longrightarrow ((1)/(3^(-2)*6^(2+3)) )^3 \rightarrow ((1)/(3^(-2)*6^(5)) )^3\\\\\text{Use rule 7 on the 3 term} \Longrightarrow ((3^(2))/(6^(5)) )^3\\\\\text{Apply rule 5} \Longrightarrow (3^(2*3))/(6^(5* 3)) \rightarrow \boxed{(3^6)/(6^(15)) } = ((6^(-3))/(3^(-2)*6^2) )^3`

Thus, the first option is correct.