Find the Exact Value ((3^-6)/(7^-3))^5

${(\frac{3^{- 6}}{7^{- 3}})}^{5}$

Step 1

Move $3^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{7^{- 3} \cdot 3^{6}})}^{5}$

Step 2

Move $7^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{7^{3}}{3^{6}})}^{5}$

Step 3

Raise $7$ to the power of $3$ .

${(\frac{343}{3^{6}})}^{5}$

Step 4

Raise $3$ to the power of $6$ .

${(\frac{343}{729})}^{5}$

Step 5

Apply the product rule to $\frac{343}{729}$ .

$\frac{343^{5}}{729^{5}}$

Step 6

Raise $343$ to the power of $5$ .

$\frac{4747561509943}{729^{5}}$

Step 7

Raise $729$ to the power of $5$ .

$\frac{4747561509943}{205891132094649}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4747561509943}{205891132094649}$

Decimal Form:

$0.02305860 \dots$