Simplify (7^87^37^4)/(7^9*7^5)

$\frac{7^{8} \cdot 7^{3} \cdot 7^{4}}{7^{9} \cdot 7^{5}}$

Step 1

Multiply $7^{8}$ by $7^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7^{8 + 3} \cdot 7^{4}}{7^{9} \cdot 7^{5}}$

Add $8$ and $3$ .

$\frac{7^{11} \cdot 7^{4}}{7^{9} \cdot 7^{5}}$

Step 2

Multiply $7^{11}$ by $7^{4}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7^{11 + 4}}{7^{9} \cdot 7^{5}}$

Add $11$ and $4$ .

$\frac{7^{15}}{7^{9} \cdot 7^{5}}$

Step 3

Multiply $7^{9}$ by $7^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7^{15}}{7^{9 + 5}}$

Add $9$ and $5$ .

$\frac{7^{15}}{7^{14}}$

Step 4

Cancel the common factor of $7^{15}$ and $7^{14}$ .

Factor $7^{14}$ out of $7^{15}$ .

$\frac{7^{14} \cdot 7}{7^{14}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{7^{14} \cdot 7}{7^{14} \cdot 1}$

Cancel the common factor.

$\frac{7^{14} \cdot 7}{7^{14} \cdot 1}$

Rewrite the expression.

$\frac{7}{1}$

Divide $7$ by $1$ .

$7$

Simplify (7^8*7^3*7^4)/(7^9*7^5)