Question

Simplify the expression answer must be in positive exponents (5a^2b^-3c^-4)^2

Answer 1

∑ Hey, jillianwagler ⊃

Answer:

`(25a^4)/(b^6c^8)`

Explanation:

Given:

Simplify the expression answer must be in positive exponents

`(5a^2b^-^3c^-^4)^2`

Solve:

Applying exponent rules~:
`\left(a\cdot \:b\right)^n=a^nb^n`

Thus,

`\left(5a^2b^(-3)c^(-4)\right)^2=5^2\left(a^2\right)^2\left(b^(-3)\right)^2\left(c^(-4)\right)^2`

`=5^2\left(a^2\right)^2\left(b^(-3)\right)^2\left(c^(-4)\right)^2`

Simplify:
`5^2=25`

Now we have;

`=25\left(a^2\right)^2\left(b^(-3)\right)^2\left(c^(-4)\right)^2`

Simplify:
`(a^2)^2:a^4`

`=25a^4\left(b^(-3)\right)^2\left(c^(-4)\right)^2`

Simplify:
`(b^-^3)^2:(1)/(b^6)`

`=25a^4(1)/(b^6)\left(c^(-4)\right)^2`

Simplify:
`(c^(-4)\right))^2:(1)/(c^8)`

`=25a^4(1)/(b^6)\cdot (1)/(c^8)`

Simplify again:

`=(25a^4)/(b^6c^8)`

Finally Answer:
`=(25a^4)/(b^6c^8)`

xcookiex12

8/19/2022