Evaluate
\frac{1024x^{10}}{59049}-\frac{256x^{8}}{6561}
Expand
\frac{1024x^{10}}{59049}-\frac{256x^{8}}{6561}
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\left(\frac{10}{15}x\right)^{10}-\left(\frac{1}{1.5}x\right)^{8}
Expand \frac{1}{1.5} by multiplying both numerator and the denominator by 10.
\left(\frac{2}{3}x\right)^{10}-\left(\frac{1}{1.5}x\right)^{8}
Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.
\left(\frac{2}{3}\right)^{10}x^{10}-\left(\frac{1}{1.5}x\right)^{8}
Expand \left(\frac{2}{3}x\right)^{10}.
\frac{1024}{59049}x^{10}-\left(\frac{1}{1.5}x\right)^{8}
Calculate \frac{2}{3} to the power of 10 and get \frac{1024}{59049}.
\frac{1024}{59049}x^{10}-\left(\frac{10}{15}x\right)^{8}
Expand \frac{1}{1.5} by multiplying both numerator and the denominator by 10.
\frac{1024}{59049}x^{10}-\left(\frac{2}{3}x\right)^{8}
Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.
\frac{1024}{59049}x^{10}-\left(\frac{2}{3}\right)^{8}x^{8}
Expand \left(\frac{2}{3}x\right)^{8}.
\frac{1024}{59049}x^{10}-\frac{256}{6561}x^{8}
Calculate \frac{2}{3} to the power of 8 and get \frac{256}{6561}.
\left(\frac{10}{15}x\right)^{10}-\left(\frac{1}{1.5}x\right)^{8}
Expand \frac{1}{1.5} by multiplying both numerator and the denominator by 10.
\left(\frac{2}{3}x\right)^{10}-\left(\frac{1}{1.5}x\right)^{8}
Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.
\left(\frac{2}{3}\right)^{10}x^{10}-\left(\frac{1}{1.5}x\right)^{8}
Expand \left(\frac{2}{3}x\right)^{10}.
\frac{1024}{59049}x^{10}-\left(\frac{1}{1.5}x\right)^{8}
Calculate \frac{2}{3} to the power of 10 and get \frac{1024}{59049}.
\frac{1024}{59049}x^{10}-\left(\frac{10}{15}x\right)^{8}
Expand \frac{1}{1.5} by multiplying both numerator and the denominator by 10.
\frac{1024}{59049}x^{10}-\left(\frac{2}{3}x\right)^{8}
Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.
\frac{1024}{59049}x^{10}-\left(\frac{2}{3}\right)^{8}x^{8}
Expand \left(\frac{2}{3}x\right)^{8}.
\frac{1024}{59049}x^{10}-\frac{256}{6561}x^{8}
Calculate \frac{2}{3} to the power of 8 and get \frac{256}{6561}.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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