MATH SOLVE

4 months ago

Q:
# Apply the properties of exponents to rewrite each expression in the form kkxxnn, where nn is an integer and x ≠0 (x^2/4x^−1)^−3

Accepted Solution

A:

Answer:[tex]64x^{-9}[/tex]Step-by-step explanation:Here, in this given problem, we have to apply the properties of indices or properties of exponents to write the following expression [tex](\frac{x^{2} }{4x^{-1} }) ^{-3}[/tex]
in the form kkxxnn, where nn is an integer and x ≠ 0.
Now, [tex](\frac{x^{2} }{4x^{-1} }) ^{-3}[/tex]
=[tex](\frac{x^{2-(-1)} }{4} )^{-3}[/tex]
{Since we know the property of exponent [tex]\frac{x^{a} }{x^{b} } =x^{(a-b)}[/tex]}
=[tex](\frac{x^{3} }{4}) ^{-3}[/tex]
=[tex](\frac{4}{x^{3} } )^{3}[/tex] {Since we know the property of exponent [tex]x^{-a}= \frac{1}{x^{a} }[/tex]}
=[tex]\frac{64}{x^{3*3} }[/tex] {Since we know the property of indices [tex](x^{a}) ^{b} =x^{ab}[/tex]}
=[tex]64x^{-9}[/tex] (Answer)