Question

Anyone know what the answer to this is?

Answer 1

it's the 3rd answer


`1 / (36a^(4){b}^(10) )`

Answer 2

Answer:
`\bold{c)\ (1)/(36\cdot a^(4)\cdot b^(10))}`

Explanation:

Use the power rule for exponents - (multiply the exponents).

Then move all of the terms that have a negative exponent to the other side of the fraction bar and change the sign of the exponent.

`\bigg(((2a^(-3)b^4)^2)/((3a^5b)^(-2))\bigg)^(-1)\\\\\\\\\text{distribute the exponent of -1 to both the top and bottom of the fraction:}\\=((2a^(-3)b^4)^(-2))/((3a^5b)^(2))\\\\\\\text{Now, distribute the exponent of -2 to the top and 2 to the bottom:}\\=(2^(-2)\cdot a^(6)\cdot b^(-8))/(3^2\cdot a^(10)\cdot b^2)`

`\text{Next, move }2^(-2)\ \text{and}\ b^(-8)\ \text{to the other side of the fraction}\\\text{bar and change the sign of the exponent.}\\\\=(a^6)/(2^2\cdot 3^2\cdot a^(10)\cdot b^2\cdot b^8)\\\\\\\text{Simplify }2^2\cdot3^2\ (4\cdot 9 = 36),\ \text{use the exponent rules for multiplying}\\ \text{terms that have the same base (add the exponents), and the exponent}\\\text{rules for dividing terms that have the same base (subtract the exponents).}\\\\=(1)/(36\cdot a^(10-6)\cdot b^(2+8))`

`=(1)/(36\cdot a^(4)\cdot b^(10))`