Question

Write the following as a simple fraction in lowest terms.
{(-6)^{-4} + (-6)^{-2}}/{-6^{-3}}

Answer 1

\[\large
\left((-6)^{-4} + (-6)^{-2}\right)/(-6)^{-3} \\
\text{To get rid of all the negative exponents, multiply top and bottom by } (-6)^4\\
\]

Answer 2

ok why by (-6)^4

Answer 3

The exponents are -2, -3, -4. If I multiply by the exponent +4, all three of the negative will become positive (or zero) because in a multiplication the exponents add.
-2 + 4 = +2
-3 + 4 = +1
-4 + 4 = 0

Answer 4

ok that makes sense

Answer 5

\[\large
\frac{(-6)^{-4} + (-6)^{-2}} {(-6)^{-3}} =
\frac{(-6)^{-4} + (-6)^{-2}} {(-6)^{-3}}*\frac{(-6)^4}{(-6)^4} = \\ \large
\frac{(-6)^{0} + (-6)^{2}} {(-6)^{1}} = \frac{1+36}{-6} = -\frac{37}{6}

\\
\]

Answer 6

ok thank you so much for your help that makes so much more sense

Answer 7

You are welcome.