Answer: [tex]\bold{\dfrac{81}{4t^2u^{20}}}[/tex]
Step-by-step explanation:
[tex]\bigg[\dfrac{4\cdot t^{-1}\cdot u^6}{18\cdot t^{-2}\cdot u^{-4}}\bigg]^{-2}\\\\\\\text{simplify 4 and 18 by dividing each by 2:}\\\bigg[\dfrac{2\cdot t^{-1}\cdot u^6}{9\cdot t^{-2}\cdot u^{-4}}\bigg]^{-2}\\\\\text{distribute the exponent using the power rule (multiply the exponents):}\\\dfrac{2^{-2}\cdot t^{2}\cdot u^{-12}}{9^{-2}\cdot t^{4}\cdot u^{8}}[/tex]
[tex]\text{Move the terms with negative exponents to the other side of the fraction}\\\text{bar and change the sign of the exponents:}\\\dfrac{9^2\cdot t^2}{2^2\cdot t^4\cdot u^8\cdot u^{12}}\\\\\\\text{Simplify using the multiplication rule for exponents (add the exponents)}\\\text{and the division rule of exponents (subtract the exponents):}\\\dfrac{81}{4\cdot t^{4-2}\cdot u^{8+12}}\\\\\\\text{Simplify:}\quad \dfrac{81}{4\cdot t^{2}\cdot u^{20}}[/tex]
