Evaluate (5(37^15-197^14))/(7^16+3*7^15)

$\frac{5 (3 \cdot 7^{15} - 19 \cdot 7^{14})}{7^{16} + 3 \cdot 7^{15}}$

Step 1

Simplify the numerator.

Raise $7$ to the power of $15$ .

$\frac{5 (3 \cdot 4747561509943 - 19 \cdot 7^{14})}{7^{16} + 3 \cdot 7^{15}}$

Multiply $3$ by $4747561509943$ .

$\frac{5 (14242684529829 - 19 \cdot 7^{14})}{7^{16} + 3 \cdot 7^{15}}$

Raise $7$ to the power of $14$ .

$\frac{5 (14242684529829 - 19 \cdot 678223072849)}{7^{16} + 3 \cdot 7^{15}}$

Multiply $- 19$ by $678223072849$ .

$\frac{5 (14242684529829 - 12886238384131)}{7^{16} + 3 \cdot 7^{15}}$

Subtract $12886238384131$ from $14242684529829$ .

$\frac{5 \cdot 1356446145698}{7^{16} + 3 \cdot 7^{15}}$

Step 2

Simplify the denominator.

Raise $7$ to the power of $16$ .

$\frac{5 \cdot 1356446145698}{33232930569601 + 3 \cdot 7^{15}}$

Raise $7$ to the power of $15$ .

$\frac{5 \cdot 1356446145698}{33232930569601 + 3 \cdot 4747561509943}$

Multiply $3$ by $4747561509943$ .

$\frac{5 \cdot 1356446145698}{33232930569601 + 14242684529829}$

Add $33232930569601$ and $14242684529829$ .

$\frac{5 \cdot 1356446145698}{47475615099430}$

Step 3

Reduce the expression by cancelling the common factors.

Multiply $5$ by $1356446145698$ .

$\frac{6782230728490}{47475615099430}$

Cancel the common factor of $6782230728490$ and $47475615099430$ .

Factor $6782230728490$ out of $6782230728490$ .

$\frac{6782230728490 (1)}{47475615099430}$

Cancel the common factors.

Factor $6782230728490$ out of $47475615099430$ .

$\frac{6782230728490 \cdot 1}{6782230728490 \cdot 7}$

Cancel the common factor.

$\frac{6782230728490 \cdot 1}{6782230728490 \cdot 7}$

Rewrite the expression.

$\frac{1}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7}$

Decimal Form:

$0.\overline{142857}$

Evaluate (5(3*7^15-19*7^14))/(7^16+3*7^15)