Basic Math Examples

$\frac{3^{- 5}}{{(4^{2})}^{2}} \div \frac{9^{- 2}}{{(2^{3})}^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3^{- 5}}{{(4^{2})}^{2}} \cdot \frac{{(2^{3})}^{3}}{9^{- 2}}$

Step 2

Combine.

$\frac{3^{- 5} {(2^{3})}^{3}}{{(4^{2})}^{2} \cdot 9^{- 2}}$

Step 3

Move $3^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(2^{3})}^{3}}{{(4^{2})}^{2} \cdot 9^{- 2} \cdot 3^{5}}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Rewrite $9$ as $3^{2}$ .

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

Step 4.2

Multiply the exponents in ${(3^{2})}^{- 2}$ .

Tap for more steps...

Step 4.2.1

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

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

Step 4.2.2

Multiply $2$ by $- 2$ .

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

Step 4.3

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

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

Step 4.4

Subtract $4$ from $5$ .

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply the exponents in ${(2^{3})}^{3}$ .

Tap for more steps...

Step 5.1.1

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

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

Step 5.1.2

Multiply $3$ by $3$ .

$\frac{2^{9}}{{(4^{2})}^{2} \cdot 3^{1}}$

Step 5.2

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

$\frac{512}{{(4^{2})}^{2} \cdot 3^{1}}$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

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

Tap for more steps...

Step 6.1.1

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

$\frac{512}{4^{2 \cdot 2} \cdot 3^{1}}$

Step 6.1.2

Multiply $2$ by $2$ .

$\frac{512}{4^{4} \cdot 3^{1}}$

Step 6.2

Raise $4$ to the power of $4$ .

$\frac{512}{256 \cdot 3^{1}}$

Step 6.3

Evaluate the exponent.

$\frac{512}{256 \cdot 3}$

Step 7

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 7.1

Multiply $256$ by $3$ .

$\frac{512}{768}$

Step 7.2

Cancel the common factor of $512$ and $768$ .

Tap for more steps...

Step 7.2.1

Factor $256$ out of $512$ .

$\frac{256 (2)}{768}$

Step 7.2.2

Cancel the common factors.

Tap for more steps...

Step 7.2.2.1

Factor $256$ out of $768$ .

$\frac{256 \cdot 2}{256 \cdot 3}$

Step 7.2.2.2

Cancel the common factor.

$\frac{256 \cdot 2}{256 \cdot 3}$

Step 7.2.2.3

Rewrite the expression.

$\frac{2}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$