Question

Apply the properties of exponents to rewrite each expression in the form kkxxnn, where nn is an integer and x ≠0

Answer 1

Answer:

$64x^{-9}$

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 $(\frac{x^{2} }{4x^{-1} }) ^{-3}$

in the form kkxxnn, where nn is an integer and x ≠ 0.

Now, $(\frac{x^{2} }{4x^{-1} }) ^{-3}$

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

{Since we know the property of exponent $\frac{x^{a} }{x^{b} } =x^{(a-b)}$}

=$(\frac{x^{3} }{4}) ^{-3}$

=$(\frac{4}{x^{3} } )^{3}$

{Since we know the property of exponent $x^{-a}= \frac{1}{x^{a} }$}

=$\frac{64}{x^{3*3} }$

{Since we know the property of indices $(x^{a}) ^{b} =x^{ab}$}

=$64x^{-9}$ (Answer)