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\frac{\left(3a^{2}\right)^{5}\times \left(9a^{4}\right)^{2}b^{15}}{\left(27a^{2}\right)^{3}\left(b^{5}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.
\frac{\left(3a^{2}\right)^{5}\times \left(9a^{4}\right)^{2}b^{15}}{\left(27a^{2}\right)^{3}b^{15}}
To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.
\frac{\left(9a^{4}\right)^{2}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Cancel out b^{15} in both numerator and denominator.
\frac{9^{2}\left(a^{4}\right)^{2}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Expand \left(9a^{4}\right)^{2}.
\frac{9^{2}a^{8}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.
\frac{81a^{8}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Calculate 9 to the power of 2 and get 81.
\frac{81a^{8}\times 3^{5}\left(a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Expand \left(3a^{2}\right)^{5}.
\frac{81a^{8}\times 3^{5}a^{10}}{\left(27a^{2}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.
\frac{81a^{8}\times 243a^{10}}{\left(27a^{2}\right)^{3}}
Calculate 3 to the power of 5 and get 243.
\frac{19683a^{8}a^{10}}{\left(27a^{2}\right)^{3}}
Multiply 81 and 243 to get 19683.
\frac{19683a^{18}}{\left(27a^{2}\right)^{3}}
To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.
\frac{19683a^{18}}{27^{3}\left(a^{2}\right)^{3}}
Expand \left(27a^{2}\right)^{3}.
\frac{19683a^{18}}{27^{3}a^{6}}
To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.
\frac{19683a^{18}}{19683a^{6}}
Calculate 27 to the power of 3 and get 19683.
a^{12}
Cancel out 19683a^{6} in both numerator and denominator.
\frac{\left(3a^{2}\right)^{5}\times \left(9a^{4}\right)^{2}b^{15}}{\left(27a^{2}\right)^{3}\left(b^{5}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.
\frac{\left(3a^{2}\right)^{5}\times \left(9a^{4}\right)^{2}b^{15}}{\left(27a^{2}\right)^{3}b^{15}}
To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.
\frac{\left(9a^{4}\right)^{2}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Cancel out b^{15} in both numerator and denominator.
\frac{9^{2}\left(a^{4}\right)^{2}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Expand \left(9a^{4}\right)^{2}.
\frac{9^{2}a^{8}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.
\frac{81a^{8}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Calculate 9 to the power of 2 and get 81.
\frac{81a^{8}\times 3^{5}\left(a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Expand \left(3a^{2}\right)^{5}.
\frac{81a^{8}\times 3^{5}a^{10}}{\left(27a^{2}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.
\frac{81a^{8}\times 243a^{10}}{\left(27a^{2}\right)^{3}}
Calculate 3 to the power of 5 and get 243.
\frac{19683a^{8}a^{10}}{\left(27a^{2}\right)^{3}}
Multiply 81 and 243 to get 19683.
\frac{19683a^{18}}{\left(27a^{2}\right)^{3}}
To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.
\frac{19683a^{18}}{27^{3}\left(a^{2}\right)^{3}}
Expand \left(27a^{2}\right)^{3}.
\frac{19683a^{18}}{27^{3}a^{6}}
To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.
\frac{19683a^{18}}{19683a^{6}}
Calculate 27 to the power of 3 and get 19683.
a^{12}
Cancel out 19683a^{6} in both numerator and denominator.
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}