Evaluate
\frac{64b^{3}a^{4}}{9}
Expand
\frac{64b^{3}a^{4}}{9}
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\frac{\left(3a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Divide \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} by \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} by multiplying \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} by the reciprocal of \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.
\frac{3^{2}\left(a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(3a^{5}\right)^{2}.
\frac{3^{2}a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.
\frac{9a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Calculate 3 to the power of 2 and get 9.
\frac{9a^{10}\times 8^{3}\left(b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(8b^{5}\right)^{3}.
\frac{9a^{10}\times 8^{3}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.
\frac{9a^{10}\times 512b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Calculate 8 to the power of 3 and get 512.
\frac{4608a^{10}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Multiply 9 and 512 to get 4608.
\frac{4608a^{10}b^{15}}{2^{3}\left(b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(2b^{4}\right)^{3}.
\frac{4608a^{10}b^{15}}{2^{3}b^{12}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.
\frac{4608a^{10}b^{15}}{8b^{12}\times \left(9a^{3}\right)^{2}}
Calculate 2 to the power of 3 and get 8.
\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}\left(a^{3}\right)^{2}}
Expand \left(9a^{3}\right)^{2}.
\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}a^{6}}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
\frac{4608a^{10}b^{15}}{8b^{12}\times 81a^{6}}
Calculate 9 to the power of 2 and get 81.
\frac{4608a^{10}b^{15}}{648b^{12}a^{6}}
Multiply 8 and 81 to get 648.
\frac{64b^{3}a^{4}}{9}
Cancel out 72a^{6}b^{12} in both numerator and denominator.
\frac{\left(3a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Divide \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} by \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} by multiplying \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} by the reciprocal of \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.
\frac{3^{2}\left(a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(3a^{5}\right)^{2}.
\frac{3^{2}a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.
\frac{9a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Calculate 3 to the power of 2 and get 9.
\frac{9a^{10}\times 8^{3}\left(b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(8b^{5}\right)^{3}.
\frac{9a^{10}\times 8^{3}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.
\frac{9a^{10}\times 512b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Calculate 8 to the power of 3 and get 512.
\frac{4608a^{10}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Multiply 9 and 512 to get 4608.
\frac{4608a^{10}b^{15}}{2^{3}\left(b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(2b^{4}\right)^{3}.
\frac{4608a^{10}b^{15}}{2^{3}b^{12}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.
\frac{4608a^{10}b^{15}}{8b^{12}\times \left(9a^{3}\right)^{2}}
Calculate 2 to the power of 3 and get 8.
\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}\left(a^{3}\right)^{2}}
Expand \left(9a^{3}\right)^{2}.
\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}a^{6}}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
\frac{4608a^{10}b^{15}}{8b^{12}\times 81a^{6}}
Calculate 9 to the power of 2 and get 81.
\frac{4608a^{10}b^{15}}{648b^{12}a^{6}}
Multiply 8 and 81 to get 648.
\frac{64b^{3}a^{4}}{9}
Cancel out 72a^{6}b^{12} 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}