Evaluate ((5^3)^9)÷(5^12)

${(5^{3})}^{9} \div 5^{12}$

Step 1

Rewrite the division as a fraction.

$\frac{{(5^{3})}^{9}}{5^{12}}$

Step 2

Simplify the numerator.

Multiply the exponents in ${(5^{3})}^{9}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5^{3 \cdot 9}}{5^{12}}$

Multiply $3$ by $9$ .

$\frac{5^{27}}{5^{12}}$

Raise $5$ to the power of $27$ .

$\frac{7450580596923830000}{5^{12}}$

Step 3

Reduce the expression by cancelling the common factors.

Raise $5$ to the power of $12$ .

$\frac{7450580596923830000}{244140625}$

Cancel the common factor of $7450580596923830000$ and $244140625$ .

Factor $625$ out of $7450580596923830000$ .

$\frac{625 (11920928955078128)}{244140625}$

Cancel the common factors.

Factor $625$ out of $244140625$ .

$\frac{625 \cdot 11920928955078128}{625 \cdot 390625}$

Cancel the common factor.

$\frac{625 \cdot 11920928955078128}{625 \cdot 390625}$

Rewrite the expression.

$\frac{11920928955078128}{390625}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{11920928955078128}{390625}$

Decimal Form:

$30517578125 \dots$