Question

Simplify the expression

Answer 1

\[\frac{ 1 }{ 3^{-2} } - \frac{ 1 }{ 3 } + \frac{ 1 }{ 4^{-1} }\]

Answer 2

well.. keep in mind that
\(\large {\bf \cfrac{1}{a^{-\color{red} n}}\implies \cfrac{1}{\frac{1}{a^{\color{red} n}}}\implies a^{{\color{red} n}}\qquad thus
\\ \quad \\
\cfrac{ 1 }{ 3^{-2} } - \cfrac{ 1 }{ 3 } + \cfrac{ 1 }{ 4^{-1} }\implies ?
}\)

Answer 3

can you walk me through the steps.

Answer 4

so it would be \[9 - \frac{ 1 }{ 3 } + 4\]

Answer 5

\[\frac{ 1 }{ 9 } - \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 }\]

Answer 6

well....
the previous one is correct
one sec

Answer 7

\(\large \bf {
\cfrac{1}{a^{-\color{red} n}}\implies \cfrac{1}{\frac{1}{a^{\color{red} n}}}\implies a^{{\color{red} n}}\qquad thus
\\ \quad \\
\cfrac{ 1 }{ 3^{-2} } - \cfrac{ 1 }{ 3 } + \cfrac{ 1 }{ 4^{-1} }\implies 3^{2}- \cfrac{ 1 }{ 3 } +4^1\implies 9- \cfrac{ 1 }{ 3 }+4
\\ \quad \\
{\color{brown}{ 4\to \cfrac{\cancel{ 12}}{\cancel{ 3}}=4\qquad 9\to \cfrac{\cancel{ 27}}{\cancel{ 3}}=9}}\qquad thus
\\ \quad \\
9- \cfrac{ 1 }{ 3 }+4\implies \cfrac{27}{3}- \cfrac{ 1 }{ 3 }+\cfrac{12}{3}\implies \cfrac{27-1+12}{3}
}\)

Answer 8

so for the 9 and the 4 we have to find common denominators and then add and subtract it all together.

Answer 9

so its 38/3

Answer 10

well... is one way to do it, yes
by making all common denominators, by multiplying by a value atop and bottom, yes

or you we could have simply find the LCD, and do it that way too

Answer 11

but yes, is 38/3
38 is not divisble by 3, so, it doesn't simplify further

Answer 12

\(\bf 9- \cfrac{ 1 }{ 3 }+4\implies \cfrac{9(3)-1+4(3)}{3}\implies \cfrac{27-1+12}{3}\impliedby \textit{using the LCD}\)

same 38/3 :)

Answer 13

(x^2y^-3)^2/(y^-3x^-2)^-2