Question

m7 18 hw multiplication and division with integers; writing expressions and equations (1) question 3 of 16 (1 point) | question attempt: 1 of unlimited evaluate. (-6)^2 = (-7)^3 =

Explanation:

Step1: Recall exponent rule for even - power

For any real number \(a\), \((-a)^{2n}=a^{2n}\) when \(n\) is a positive integer. Here \(a = 6\) and \(n = 1\), so \((-6)^{2}=(-6)\times(-6)\).
\((-6)\times(-6)=36\)

Step2: Recall exponent rule for odd - power

For any real number \(a\), \((-a)^{2n + 1}=-a^{2n+1}\) when \(n\) is a non - negative integer. Here \(a = 7\) and \(n = 1\), so \((-7)^{3}=(-7)\times(-7)\times(-7)\).
\((-7)\times(-7)=49\), and \(49\times(-7)=-343\)

Answer:

\((-6)^{2}=36\)
\((-7)^{3}=-343\)