Question

how do you solve the following using properties of exponents...... -6(2x^-3)^2/10x^-2

Answer 1

some properties we will need for this problem:
\[(n ^{a})^b=n ^{a*b}\]

Answer 2

\[\frac{ 1 }{ x ^{-a} }=\frac{ x ^{a}}{ 1 } =x^a\]
\[\frac{ 1 }{ x^a }=\frac{ x ^{-a} }{ 1 }=x^{-a}\]

Answer 3

we will also have to factor all of the numbers present in this fraction into lowest prime factorization form

Answer 4

6=2*3
10=2*5

Answer 5

oops, more properties

Answer 6

\[\frac{x ^{a}}{x ^{b}}=x ^{a-b} AND \frac{x^{a}}{x^{-b}}=x^{a+b}\]

Answer 7

\[\frac{ -6*(2x^{-3})^{2} }{ 10*x^{-2} }=\frac{ -6*2^2*x^{-6} }{ 10*x^{-2} }\]

Answer 8

\[\frac{−6∗2^2*x^{−6}}{10∗x^{−2}}=\frac{−6∗2^2*x^{(2−6)}}{10}=\frac{−6∗2^2*x^{-4}}{10}\]

Answer 9

\[\frac{−6∗2^2*x^{-4}}{10}=\frac{−2*3∗2^2*x^{-4}}{2*5}=\frac{−3∗2^2*x^{-4}}{5}=\frac{−2^2*3}{5}*x^{-4}=\frac{-12}{5}*x^{-4}\]