The equation m^(2/3) + 10m^(1/3) + 9 = 0 is said to be in __________form, because making the substitution u = __________results in a new equation that is quadratic.

In mathematical expressions/equations, power to which a variable has been raised is called an exponent or index.
Any indicial equation which can be converted to a quadratic equation using proper substitution can be said to be in “quadratic-form”.
Equation given can be rearranged as:
${\displaystyle m^{\frac{2}{3}}+10m^{\frac{1}{3}}+9=0}$
${\displaystyle \iff {\left(m^{\frac{1}{3}}\right)}^2+10\left(m^{\frac{1}{3}}\right)+9=0}$
If we make the substitution:
${\displaystyle u=m^{\frac{1}{3}}}$
The given equation can be transformed into quadratic equation in variable u as shown:
${\displaystyle {\left(m^{\frac{1}{3}}\right)}^2+10\left(m^{\frac{1}{3}}\right)+9=0}$
${\displaystyle \iff u^2+10u+9=0}$
Answer:
The equation ${\displaystyle m^{\frac{2}{3}}+10m^{\frac{1}{3}}+9=0}$ is said to be in quadratic form, because making the substitution ${\displaystyle u=m^{\frac{1}{3}}}$ results in a new equation that is quadratic.