Question

Evaluate the expression 6x^2y^-3 for x=4 and y=-2

Answer 1

`\boxed{\bold{-12}}`

Explanation:

Rewrite Equation

`\bold{\left(6\cdot \:4^2\right)\left(-2^(-3)\right)}`

Remove Parenthesis: (a) = a

`\bold{-6\cdot \:4^2\cdot \:2^(-3)}`

Factor Integer:
`\bold{6=2\cdot \:3}`

`\bold{-2\cdot \:3\cdot \:4^2\cdot \:2^(-3)}`

Factor Integer:
`\bold{4=2^2}`

`\bold{-2\cdot \:3\left(2^2\right)^2\cdot \:2^(-3)}`

Apply Exponent Rule
`\bold{\left(a^b\right)^c=a^(bc): \ \left(2^2\right)^2=2^(2\cdot \:2)}`

`\bold{-2\cdot \:3\cdot \:2^(2\cdot \:2)\cdot \:2^(-3)}`

Refine

`\bold{-2\cdot \:3\cdot \:2^4\cdot \:2^(-3)}`

Apply Exponent Rule
`\bold{\:a^b\cdot \:a^c=a^(b+c): \ 2^(-3)\cdot \:2^4\cdot \:2=\:2^(1+4-3)=\:2^2}`

`\bold{-2^2\cdot \:3}`

Simplify
`\bold{2^2=4}`

`\bold{-3\cdot \:4}`

Multiply:
`\bold{3\cdot \:4=12}`

Apply Negative Sign

`\bold{-12}`