Đáp án:

$\bigg(\dfrac{1}{4x^3}-2x^4 \bigg)^4=16x^{16}+\dfrac{1}{256x^{12}}-\dfrac{1}{8x^5}+\dfrac{3}{2}x^2-8x^9+16x^{16}$

Giải thích các bước giải:

$\bigg(\dfrac{1}{4x^3}-2x^4 \bigg)^4\ (x \neq 0)$

$=C_{4}^0 \bigg(\dfrac{1}{4x^3} \bigg)^4 \big(2x^4 \big)^0-C_{4}^1 \bigg(\dfrac{1}{4x^3} \bigg)^3 \big(2x^4 \big)^1+C_{4}^2 \bigg(\dfrac{1}{4x^3} \bigg)^2 \big(2x^4 \big)^2-C_{4}^3 \bigg(\dfrac{1}{4x^3} \bigg)^1 \big(2x^4 \big)^3+C_{4}^4 \bigg(\dfrac{1}{4x^3} \bigg)^0 \big(2x^4 \big)^4$

$=\dfrac{1}{256x^{12}}-8x^4. \bigg(\dfrac{1}{64x^9} \bigg)+24x^8. \bigg(\dfrac{1}{16x^6} \bigg)-32x^{12}. \dfrac{1}{4x^3}+16x^{16}$

$=16x^{16}+\dfrac{1}{256x^{12}}-\dfrac{1}{8x^5}+\dfrac{3}{2}x^2-8x^9+16x^{16}$