Question

What’s the answer to this and working out

Answer 1

Answer:
`\bold{(81)/(4t^2u^(20))}`

Explanation:

`\bigg[(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[(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):}\\(2^(-2)\cdot t^(2)\cdot u^(-12))/(9^(-2)\cdot t^(4)\cdot u^(8))`

`\text{Move the terms with negative exponents to the other side of the fraction}\\\text{bar and change the sign of the exponents:}\\(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):}\\(81)/(4\cdot t^(4-2)\cdot u^(8+12))\\\\\\\text{Simplify:}\quad (81)/(4\cdot t^(2)\cdot u^(20))`