Question

Can anyone help!
1. Simplify each equation. show all work, step-by-step.
a. sqrt6w^3 * sqrt12w
b. (125)^-2\3
2.Simplify each expression. Rationalize denominators. Show all work, step-by-step.
a.10/sqrt5
b.sqrt w^4/x^3

Answer 1

\[\frac{ a^b }{ a^g } = a^{b-g}\]
Similarly: \[\frac{ 1 }{ \sqrt{a} } = a^{- \frac{ 1 }{ 2 }}\]

Answer 2

How would I use that?

Answer 3

Well, you would use that for the 1st and last question.

Answer 4

It might also help if you know that \[\frac{ 1 }{ a^2 } = a^{-2}\]

Answer 5

so would the sqrt 6w^3 go over sqrt 12w

Answer 6

1.a)\[\sqrt{6w^3}\times \sqrt{12w}\]
\[=w \sqrt{6w}\times2\sqrt{3w}\]
\[=2w \sqrt{18w^2}\]
\[=6w^2\sqrt{2}\]
b)\[(125)^{-\frac{ 2 }{ 3 }}\]
\[=\frac{ 1 }{ \sqrt[3]{(125)^2} }\]
\[=\frac{ 1 }{ 25 }\]

Answer 7

2. a)\[\frac{ 10 }{\sqrt5 }\times \frac{ \sqrt5 }{ \sqrt5 }\]
\[=\frac{ 10\sqrt5 }{ 5 }\]
\[=2\sqrt5\]

Answer 8

b)\[\sqrt{\frac{ w^4 }{ x^3 }}\]
\[=\frac{ w }{ x }\sqrt{\frac{ w^2 }{ x }}\]
\[=\frac{ w \sqrt{w^2} }{ x \sqrt{x} }\times \frac{ \sqrt{x} }{ \sqrt{x} }\]
\[=\frac{ w^2 \sqrt{x} }{ x^2 }\]