Evaluate
ma^{\frac{10}{3}}
Differentiate w.r.t. m
a^{\frac{10}{3}}
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\frac{\frac{ma^{\frac{1}{3}}}{9nb}}{\frac{\left(3n^{\frac{1}{2}}a^{\frac{3}{2}}\right)^{-2}}{\left(b^{-\frac{1}{2}}\right)^{-2}}}
To raise \frac{3n^{\frac{1}{2}}a^{\frac{3}{2}}}{b^{-\frac{1}{2}}} to a power, raise both numerator and denominator to the power and then divide.
\frac{ma^{\frac{1}{3}}\left(b^{-\frac{1}{2}}\right)^{-2}}{9nb\times \left(3n^{\frac{1}{2}}a^{\frac{3}{2}}\right)^{-2}}
Divide \frac{ma^{\frac{1}{3}}}{9nb} by \frac{\left(3n^{\frac{1}{2}}a^{\frac{3}{2}}\right)^{-2}}{\left(b^{-\frac{1}{2}}\right)^{-2}} by multiplying \frac{ma^{\frac{1}{3}}}{9nb} by the reciprocal of \frac{\left(3n^{\frac{1}{2}}a^{\frac{3}{2}}\right)^{-2}}{\left(b^{-\frac{1}{2}}\right)^{-2}}.
\frac{ma^{\frac{1}{3}}b^{1}}{9nb\times \left(3n^{\frac{1}{2}}a^{\frac{3}{2}}\right)^{-2}}
To raise a power to another power, multiply the exponents. Multiply -\frac{1}{2} and -2 to get 1.
\frac{ma^{\frac{1}{3}}b}{9nb\times \left(3n^{\frac{1}{2}}a^{\frac{3}{2}}\right)^{-2}}
Calculate b to the power of 1 and get b.
\frac{ma^{\frac{1}{3}}b}{9nb\times 3^{-2}\left(n^{\frac{1}{2}}\right)^{-2}\left(a^{\frac{3}{2}}\right)^{-2}}
Expand \left(3n^{\frac{1}{2}}a^{\frac{3}{2}}\right)^{-2}.
\frac{ma^{\frac{1}{3}}b}{9nb\times 3^{-2}n^{-1}\left(a^{\frac{3}{2}}\right)^{-2}}
To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and -2 to get -1.
\frac{ma^{\frac{1}{3}}b}{9nb\times 3^{-2}n^{-1}a^{-3}}
To raise a power to another power, multiply the exponents. Multiply \frac{3}{2} and -2 to get -3.
\frac{ma^{\frac{1}{3}}b}{9nb\times \frac{1}{9}n^{-1}a^{-3}}
Calculate 3 to the power of -2 and get \frac{1}{9}.
\frac{ma^{\frac{1}{3}}b}{nbn^{-1}a^{-3}}
Multiply 9 and \frac{1}{9} to get 1.
\frac{ma^{\frac{1}{3}}b}{ba^{-3}}
Multiply n and n^{-1} to get 1.
\frac{\sqrt[3]{a}m}{a^{-3}}
Cancel out b in both numerator and denominator.
ma^{\frac{10}{3}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}