Question

Multiplicative inverse of (7/3)^-3

Answer 1

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!

Answer 2

Hello.

First, let's calculate

$\tt{\displaystyle(\frac{7}{3}) ^{-3}$

Remember the Properties of Exponents:

If we have a number to a negative power, we flop the number over:

$\tt{a^{-b}=\displaystyle\frac{1}{a^b}$

Now, let's use this property to simplify our expression.

Flop the number over:

$\tt{\displaystyle(\frac{3}{7} )^3$

Now, we should recall another property of exponents:

$\tt{\displaystyle(\frac{a}{b} )^m=\frac{a^m}{b^m}$

Since we have a fraction to a power, we should raise both the numerator and the denominator to the power:

$\tt{\displaystyle\frac{3^3}{7^3}$

3 cubed is 9, and 7 cubed is 343:

$\tt{\displaystyle\frac{9}{343}$

Now, the multiplicative inverse of that number is simply that number flopped over:

$\Large\boxed{\tt{\displaystyle\frac{343}{9} }}$

I hope it helps.

Have a great day.

$\boxed{imperturbability}$