If h=a^-3 and am=1 what does h^3 equal in terms of m?

The fact that am = 1 tells you that a and m are reciprocals. In other words, m=\dfrac{1}{a}.

Since you know that h=a^{-3}, you know that h=\left(\dfrac{1}{a}\right)^3.

You can use the fact that a and m are reciprocals to substitute:h=m^3.

So, h^3=\left(m^3\right)^3=m^9.

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