Basic Math Examples

$\frac{2^{3} \cdot {(- 3)}^{2} \cdot 4^{2}}{6^{3} \cdot 9^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $4$ as $2^{2}$ .

$\frac{{(2^{2})}^{2} \cdot 2^{3} \cdot {(- 3)}^{2}}{6^{3} \cdot 9^{2}}$

Step 1.2

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

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Step 1.2.1

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

$\frac{2^{2 \cdot 2} \cdot 2^{3} \cdot {(- 3)}^{2}}{6^{3} \cdot 9^{2}}$

Step 1.2.2

Multiply $2$ by $2$ .

$\frac{2^{4} \cdot 2^{3} \cdot {(- 3)}^{2}}{6^{3} \cdot 9^{2}}$

Step 1.3

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

$\frac{2^{4 + 3} \cdot {(- 3)}^{2}}{6^{3} \cdot 9^{2}}$

Step 1.4

Add $4$ and $3$ .

$\frac{2^{7} \cdot {(- 3)}^{2}}{6^{3} \cdot 9^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $6$ to the power of $3$ .

$\frac{2^{7} \cdot {(- 3)}^{2}}{216 \cdot 9^{2}}$

Step 2.2

Raise $9$ to the power of $2$ .

$\frac{2^{7} \cdot {(- 3)}^{2}}{216 \cdot 81}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $2$ to the power of $7$ .

$\frac{128 {(- 3)}^{2}}{216 \cdot 81}$

Step 3.2

Raise $- 3$ to the power of $2$ .

$\frac{128 \cdot 9}{216 \cdot 81}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Multiply $216$ by $81$ .

$\frac{128 \cdot 9}{17496}$

Step 4.2

Multiply $128$ by $9$ .

$\frac{1152}{17496}$

Step 4.3

Cancel the common factor of $1152$ and $17496$ .

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Step 4.3.1

Factor $72$ out of $1152$ .

$\frac{72 (16)}{17496}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $72$ out of $17496$ .

$\frac{72 \cdot 16}{72 \cdot 243}$

Step 4.3.2.2

Cancel the common factor.

$\frac{72 \cdot 16}{72 \cdot 243}$

Step 4.3.2.3

Rewrite the expression.

$\frac{16}{243}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{243}$

Decimal Form:

$0.06584362 \dots$