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[tex] n^{-6} [/tex] x 1
any expression multiplied by 1 remains the same
m³[tex] n^{-6} [/tex]
now express this with a positive exponent using [tex] a^{-n} [/tex] = [tex] \frac{1}{ a^{n} } [/tex]
m³ x [tex] \frac{1}{ n^{6} } [/tex]
now calculate the product
[tex] \frac{m^{3} }{ n^{6} } [/tex]
this means that the correct answer to number one is [tex] \frac{m^{3} }{ n^{6} } [/tex]
2) the first step for solving this expression is to reduce the fraction with a
[tex] \frac{ a^{3} b^{-3} }{ b^{-2} } [/tex]
now reduce the fraction with [tex] b^{-3} [/tex]
[tex] \frac{a^{3} }{b} [/tex]
this means that the correct answer to question 2 is [tex] \frac{a^{3} }{b} [/tex]
3) the first step to solving this expression is to express with a positive exponent using tex] a^{-n} [/tex] = [tex] \frac{1}{ a^{n} } [/tex]
([tex] x^{-2} [/tex] × [tex] \frac{1}{ y^{4} } [/tex] × x³ ) [tex] ^{-2} [/tex]
now calculate the product
([tex] \frac{x}{y^{4} } )^{-2} [/tex]
now express with a positive exponent using ([tex] \frac{a}{b}[/tex])[tex] [tex] x^{-n} [/tex] = ([tex] \frac{b}{a} [/tex])[tex] ^{n} [/tex]
([tex] \frac{y^{4} }{x} [/tex])[tex] ^{2} [/tex]
to raise a fraction to a power,, you need to raise the numerator and denominator to that power.
[tex] \frac{y^{8} }{ x^{2} } [/tex]
this means that the correct answer to question 3 is [tex] \frac{y^{8} }{ x^{2} } [/tex]
let me know if you have any further questions
:)
