# 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.

The equation ${m}^{\frac{2}{3}}+10{m}^{\frac{1}{3}}+9=0$ is said to be in __________form, because making the substitution u = __________results in a new equation that is quadratic.
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Luvottoq
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:
${m}^{\frac{2}{3}}+10{m}^{\frac{1}{3}}+9=0$
$⇔{\left({m}^{\frac{1}{3}}\right)}^{2}+10\left({m}^{\frac{1}{3}}\right)+9=0$
If we make the substitution:
$u={m}^{\frac{1}{3}}$
The given equation can be transformed into quadratic equation in variable u as shown:
${\left({m}^{\frac{1}{3}}\right)}^{2}+10\left({m}^{\frac{1}{3}}\right)+9=0$
$⇔{u}^{2}+10u+9=0$
The equation ${m}^{\frac{2}{3}}+10{m}^{\frac{1}{3}}+9=0$ is said to be in quadratic form, because making the substitution $u={m}^{\frac{1}{3}}$ results in a new equation that is quadratic.
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