Question

Simplify each expression. Use positive exponents.

Answer 1

1) the first step to solving this is to know that any non zero expression that is raised to the power of zero will equal 1.
m³
`n^(-6)` x 1
any expression multiplied by 1 remains the same
m³
`n^(-6)`
now express this with a positive exponent using
`a^(-n)` =
`(1)/( a^(n) )`
m³ x
`(1)/( n^(6) )`
now calculate the product

`(m^(3) )/( n^(6) )`
this means that the correct answer to number one is
`(m^(3) )/( n^(6) )`
2) the first step for solving this expression is to reduce the fraction with a

`( a^(3) b^(-3) )/( b^(-2) )`
now reduce the fraction with
`b^(-3)`

`(a^(3) )/(b)`
this means that the correct answer to question 2 is
`(a^(3) )/(b)`
3) the first step to solving this expression is to express with a positive exponent using tex] a^{-n} [/tex] =
`(1)/( a^(n) )`
(
`x^(-2)` ×
`(1)/( y^(4) )` × x³ )
`^(-2)`
now calculate the product
(
`(x)/(y^(4) ) )^(-2)`
now express with a positive exponent using (
`(a)/(b)`)
`[tex] x^(-n)` = (
`(b)/(a)`)
`^(n)`
(
`(y^(4) )/(x)`)
`^(2)`
to raise a fraction to a power,, you need to raise the numerator and denominator to that power.

`(y^(8) )/( x^(2) )`
this means that the correct answer to question 3 is
`(y^(8) )/( x^(2) )`
let me know if you have any further questions
:)

Answer 2

1.

`m {}^(3) n {}^( - 6) p {}^(0) = m {}^(3) \frac{1}{ {n}^(6) } * 1 = \frac{ {m}^(3) }{ {n}^(6) }`

2.

`\frac{a {}^(4) {b}^( - 3) }{ab {}^( - 2) } = \frac{a {}^(4) {b}^(2) }{a {b}^(3 ) } = \frac{ {a}^(3) }{b}`


3.

`( {x}^( - 2) y {}^( - 4) x {}^(3) ) {}^( - 2) =( \frac{1}{ {x}^(2) } \frac{1}{ {y}^(4) } {x}^(3) ) {}^( - 2) = \\ ( \frac{1}{ {y}^(4) } x) {}^( - 2)`

`= ( \frac{x}{ {y}^(4) } ) {}^( -2 ) = ( (4y)/(x) ) {}^(2) = ( \frac{y {}^(8) }{x {}^(2) } )`





good luck