How do you simplify \frac { 3^ { 9} \cdot 3^ { 7} } { ( 3^ { 3} ) ^ { 4} }?

Feb 22, 2017

${3}^{4}$

Explanation:

Using Law of addition of exponents in the numerator and law of multiplication of exponents in the denominator, it is
$\frac{{3}^{16}}{3} ^ 12$

Next using law of subtraction of exponents, it is=${3}^{16 - 12} = {3}^{4}$

Feb 22, 2017

$81$

Explanation:

Some rules to take note of:

${a}^{b} \cdot {a}^{c} = {a}^{b + c}$

${\left({a}^{b}\right)}^{c} = {a}^{b \cdot c}$

$\frac{{a}^{b}}{{a}^{c}} = {a}^{b - c}$

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So now, let's apply them:

$\frac{{3}^{9} \cdot {3}^{7}}{{\left({3}^{3}\right)}^{4}}$

Using the first rule, simplify the numerator.

$\frac{{3}^{16}}{{\left({3}^{3}\right)}^{4}}$

Now apply the second rule to the denominator.

$\frac{{3}^{16}}{{3}^{12}}$

Finally, apply the third rule to the entire fraction.

${3}^{4}$

To get the final answer, do the operation:

$3 \cdot 3 \cdot 3 \cdot 3 = 81$