Question

-729÷64 express it in exponential form

Answer 1

$\underline{\mathfrak{\huge{Question:}}}$

Convert the term :- $\frac{(-729)}{64}$ into it's exponential form.

$\underline{\mathfrak{\huge{Answer:}}}$

Now, we already know that :-

729 = 9 × 9 × 9

Thus :-

=》 729 = $9^{3}$

And we also know that :-

9 × 9 × 9 = 3 × 3 × 3 × 3 × 3 × 3

So, by this discussion, we can say that :-

$\tt{729 = 3^{6}}$

Another number that we're given with is = 64

About 64, we know that :-

64 = 8 × 8

Thus :-

=》 64 = $8^{2}$

An we also know that :-

8 × 8 = 2 × 2 × 2 × 2 × 2 × 2

So, by this discussion, we can say that :-

$\tt{64 = 2^{6}}$

Now, coming in the term we were given with :-

$-(\frac{729}{64})$

This term will be = $\tt{-(\frac{3^{6}}{2^{6})}}$

This can also be written as :-

=》 $\tt{{-(\frac{3}{2})}^{6}}$

That will be your final answer !

Answer 2

Express the following in exponential form.

$\tt{ \frac{ - 729}{64}}$

Step by step explanation :

We already know that,

729 = 9 × 9 × 9

We can also write this as :

9 × 9 × 9 = 3 × 3 × 3 × 3 × 3 × 3

Thus,

Expressing this in a^m form, we get :

$\tt{3 × 3 × 3 × 3 × 3 × 3 = 3 {}^{6}}$

Now,

Similarly,

We can write 64 as :

8 × 8

We can also write this as :

8 × 8 = 2 × 2 × 2 × 2 × 2 × 2

Thus, Expressing this in a^m form,

$\tt{2 × 2 × 2 × 2 × 2 × 2 = 2 {}^{6}}$

Thus, We got the fraction :

$\tt{ - ( \frac{3 {}^{6} }{2 {}^{6} } )}$

We know that,

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

So,

Final answer is as follows :

$\tt{ = - ( \frac{3}{2}) {}^{6} }$