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\frac{\left(2x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{\left(x^{-4}\right)^{-2}}-4x^{-12}\left(x^{-2}\right)^{-7}
To raise a power to another power, multiply the exponents. Multiply -2 and -5 to get 10.
\frac{\left(2x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{-12}\left(x^{-2}\right)^{-7}
To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.
\frac{\left(2x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{-12}x^{14}
To raise a power to another power, multiply the exponents. Multiply -2 and -7 to get 14.
\frac{\left(2x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{2}
To multiply powers of the same base, add their exponents. Add -12 and 14 to get 2.
\frac{2^{3}\left(x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{2}
Expand \left(2x^{2}\right)^{3}.
\frac{2^{3}x^{6}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{2}
To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.
\frac{8x^{6}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{2}
Calculate 2 to the power of 3 and get 8.
8x^{2}+\frac{3x^{10}}{x^{8}}-4x^{2}
Cancel out x^{4} in both numerator and denominator.
8x^{2}+3x^{2}-4x^{2}
Cancel out x^{8} in both numerator and denominator.
11x^{2}-4x^{2}
Combine 8x^{2} and 3x^{2} to get 11x^{2}.
7x^{2}
Combine 11x^{2} and -4x^{2} to get 7x^{2}.
\frac{\left(2x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{\left(x^{-4}\right)^{-2}}-4x^{-12}\left(x^{-2}\right)^{-7}
To raise a power to another power, multiply the exponents. Multiply -2 and -5 to get 10.
\frac{\left(2x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{-12}\left(x^{-2}\right)^{-7}
To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.
\frac{\left(2x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{-12}x^{14}
To raise a power to another power, multiply the exponents. Multiply -2 and -7 to get 14.
\frac{\left(2x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{2}
To multiply powers of the same base, add their exponents. Add -12 and 14 to get 2.
\frac{2^{3}\left(x^{2}\right)^{3}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{2}
Expand \left(2x^{2}\right)^{3}.
\frac{2^{3}x^{6}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{2}
To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.
\frac{8x^{6}}{x^{4}}+\frac{3x^{10}}{x^{8}}-4x^{2}
Calculate 2 to the power of 3 and get 8.
8x^{2}+\frac{3x^{10}}{x^{8}}-4x^{2}
Cancel out x^{4} in both numerator and denominator.
8x^{2}+3x^{2}-4x^{2}
Cancel out x^{8} in both numerator and denominator.
11x^{2}-4x^{2}
Combine 8x^{2} and 3x^{2} to get 11x^{2}.
7x^{2}
Combine 11x^{2} and -4x^{2} to get 7x^{2}.