Respuesta :
Hello.
First, let's calculate
[tex]\tt{\displaystyle(\frac{7}{3}) ^{-3}[/tex]
Remember the Properties of Exponents:
If we have a number to a negative power, we flop the number over:
[tex]\tt{a^{-b}=\displaystyle\frac{1}{a^b}[/tex]
Now, let's use this property to simplify our expression.
Flop the number over:
[tex]\tt{\displaystyle(\frac{3}{7} )^3[/tex]
Now, we should recall another property of exponents:
[tex]\tt{\displaystyle(\frac{a}{b} )^m=\frac{a^m}{b^m}[/tex]
Since we have a fraction to a power, we should raise both the numerator and the denominator to the power:
[tex]\tt{\displaystyle\frac{3^3}{7^3}[/tex]
3 cubed is 9, and 7 cubed is 343:
[tex]\tt{\displaystyle\frac{9}{343}[/tex]
Now, the multiplicative inverse of that number is simply that number flopped over:
[tex]\Large\boxed{\tt{\displaystyle\frac{343}{9} }}[/tex]
I hope it helps.
Have a great day.
[tex]\boxed{imperturbability}[/tex]
Hi there! I am EnjoyingLife, and I hope you find my answer helpful! :)
STEPS:
First we have a negative power so we flop the number over
Then since we have a fraction to a power we raise both the top & bottom to that power.
Then, we flop the number over once more to find the multiplicative inverse.
Hope it helps!
