Simplify (5^56^38^10)/(5^368^9)

$\frac{5^{5} \cdot 6^{3} \cdot 8^{10}}{5^{3} \cdot 6 \cdot 8^{9}}$

Step 1

Cancel the common factor of $5^{5}$ and $5^{3}$ .

Factor $5^{3}$ out of $5^{5} \cdot 6^{3} \cdot 8^{10}$ .

$\frac{5^{3} (5^{2} \cdot 6^{3} \cdot 8^{10})}{5^{3} \cdot 6 \cdot 8^{9}}$

Cancel the common factors.

Factor $5^{3}$ out of $5^{3} \cdot 6 \cdot 8^{9}$ .

$\frac{5^{3} (5^{2} \cdot 6^{3} \cdot 8^{10})}{5^{3} (6 \cdot 8^{9})}$

Cancel the common factor.

$\frac{5^{3} (5^{2} \cdot 6^{3} \cdot 8^{10})}{5^{3} (6 \cdot 8^{9})}$

Rewrite the expression.

$\frac{5^{2} \cdot 6^{3} \cdot 8^{10}}{6 \cdot 8^{9}}$

Step 2

Cancel the common factor of $6^{3}$ and $6$ .

Factor $6$ out of $5^{2} \cdot 6^{3} \cdot 8^{10}$ .

$\frac{6 (5^{2} \cdot 6^{2} \cdot 8^{10})}{6 \cdot 8^{9}}$

Cancel the common factors.

Factor $6$ out of $6 \cdot 8^{9}$ .

$\frac{6 (5^{2} \cdot 6^{2} \cdot 8^{10})}{6 (8^{9})}$

Cancel the common factor.

$\frac{6 (5^{2} \cdot 6^{2} \cdot 8^{10})}{6 \cdot 8^{9}}$

Rewrite the expression.

$\frac{5^{2} \cdot 6^{2} \cdot 8^{10}}{8^{9}}$

Step 3

Cancel the common factor of $8^{10}$ and $8^{9}$ .

Factor $8^{9}$ out of $5^{2} \cdot 6^{2} \cdot 8^{10}$ .

$\frac{8^{9} (5^{2} \cdot 6^{2} \cdot 8)}{8^{9}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{8^{9} (5^{2} \cdot 6^{2} \cdot 8)}{8^{9} \cdot 1}$

Cancel the common factor.

$\frac{8^{9} (5^{2} \cdot 6^{2} \cdot 8)}{8^{9} \cdot 1}$

Rewrite the expression.

$\frac{5^{2} \cdot 6^{2} \cdot 8}{1}$

Divide $5^{2} \cdot 6^{2} \cdot 8$ by $1$ .

$5^{2} \cdot 6^{2} \cdot 8$

Step 4

Evaluate the exponents.

Raise $5$ to the power of $2$ .

$25 \cdot 6^{2} \cdot 8$

Raise $6$ to the power of $2$ .

$25 \cdot 36 \cdot 8$

Step 5

Multiply $25 \cdot 36 \cdot 8$ .

Multiply $25$ by $36$ .

$900 \cdot 8$

Multiply $900$ by $8$ .

$7200$

Simplify (5^5*6^3*8^10)/(5^3*6*8^9)

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Simplify (5^56^38^10)/(5^368^9)