Simplify ((2^157^12)/(7(2^2)^47^42))^3

${(\frac{2^{15} \cdot 7^{12}}{7 \cdot {(2^{2})}^{4} \cdot 7^{4} \cdot 2})}^{3}$

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

Move $7^{4}$ .

${(\frac{2^{15} \cdot 7^{12}}{7^{4} \cdot 7 \cdot {(2^{2})}^{4} \cdot 2})}^{3}$

Multiply $7^{4}$ by $7$ .

Raise $7$ to the power of $1$ .

${(\frac{2^{15} \cdot 7^{12}}{7^{4} \cdot 7^{1} \cdot {(2^{2})}^{4} \cdot 2})}^{3}$

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

${(\frac{2^{15} \cdot 7^{12}}{7^{4 + 1} \cdot {(2^{2})}^{4} \cdot 2})}^{3}$

Add $4$ and $1$ .

${(\frac{2^{15} \cdot 7^{12}}{7^{5} \cdot {(2^{2})}^{4} \cdot 2})}^{3}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2^{15}$ and $2$ .

Factor $2$ out of $2^{15} \cdot 7^{12}$ .

${(\frac{2 (2^{14} \cdot 7^{12})}{7^{5} \cdot {(2^{2})}^{4} \cdot 2})}^{3}$

Cancel the common factors.

Factor $2$ out of $7^{5} \cdot {(2^{2})}^{4} \cdot 2$ .

${(\frac{2 (2^{14} \cdot 7^{12})}{2 \cdot (7^{5} \cdot {(2^{2})}^{4})})}^{3}$

Cancel the common factor.

${(\frac{2 (2^{14} \cdot 7^{12})}{2 \cdot (7^{5} \cdot {(2^{2})}^{4})})}^{3}$

Rewrite the expression.

${(\frac{2^{14} \cdot 7^{12}}{7^{5} \cdot {(2^{2})}^{4}})}^{3}$

Cancel the common factor of $7^{12}$ and $7^{5}$ .

Factor $7^{5}$ out of $2^{14} \cdot 7^{12}$ .

${(\frac{7^{5} (2^{14} \cdot 7^{7})}{7^{5} \cdot {(2^{2})}^{4}})}^{3}$

Cancel the common factors.

Factor $7^{5}$ out of $7^{5} \cdot {(2^{2})}^{4}$ .

${(\frac{7^{5} (2^{14} \cdot 7^{7})}{7^{5} ({(2^{2})}^{4})})}^{3}$

Cancel the common factor.

${(\frac{7^{5} (2^{14} \cdot 7^{7})}{7^{5} {(2^{2})}^{4}})}^{3}$

Rewrite the expression.

${(\frac{2^{14} \cdot 7^{7}}{{(2^{2})}^{4}})}^{3}$

Simplify the numerator.

Raise $2$ to the power of $14$ .

${(\frac{16384 \cdot 7^{7}}{{(2^{2})}^{4}})}^{3}$

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

${(\frac{16384 \cdot 823543}{{(2^{2})}^{4}})}^{3}$

Simplify the denominator.

Multiply the exponents in ${(2^{2})}^{4}$ .

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

${(\frac{16384 \cdot 823543}{2^{2 \cdot 4}})}^{3}$

Multiply $2$ by $4$ .

${(\frac{16384 \cdot 823543}{2^{8}})}^{3}$

Raise $2$ to the power of $8$ .

${(\frac{16384 \cdot 823543}{256})}^{3}$

Simplify the expression.

Multiply $16384$ by $823543$ .

${(\frac{13492928512}{256})}^{3}$

Divide $13492928512$ by $256$ .

$52706752^{3}$

Raise $52706752$ to the power of $3$ .

$146419446994248000000000$

The result can be shown in multiple forms.

Exact Form:

$146419446994248000000000$

Decimal Form:

$1.46419446 \cdot 10^{23}$

Simplify ((2^15*7^12)/(7*(2^2)^4*7^4*2))^3

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Simplify ((2^157^12)/(7(2^2)^47^42))^3