Basic Math Examples

$\frac{4^{- 6} \cdot 16^{2}}{8^{5} \cdot 4^{- 3}}$

Step 1

Move $4^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{16^{2}}{8^{5} \cdot 4^{- 3} \cdot 4^{6}}$

Step 2

Multiply $4^{- 3}$ by $4^{6}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $4^{6}$ .

$\frac{16^{2}}{8^{5} \cdot (4^{6} \cdot 4^{- 3})}$

Step 2.2

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

$\frac{16^{2}}{8^{5} \cdot 4^{6 - 3}}$

Step 2.3

Subtract $3$ from $6$ .

$\frac{16^{2}}{8^{5} \cdot 4^{3}}$

Step 3

Raise $16$ to the power of $2$ .

$\frac{256}{8^{5} \cdot 4^{3}}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Rewrite $8$ as $2^{3}$ .

$\frac{256}{{(2^{3})}^{5} \cdot 4^{3}}$

Step 4.2

Multiply the exponents in ${(2^{3})}^{5}$ .

Tap for more steps...

Step 4.2.1

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

$\frac{256}{2^{3 \cdot 5} \cdot 4^{3}}$

Step 4.2.2

Multiply $3$ by $5$ .

$\frac{256}{2^{15} \cdot 4^{3}}$

Step 4.3

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

$\frac{256}{2^{15} \cdot {(2^{2})}^{3}}$

Step 4.4

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

Tap for more steps...

Step 4.4.1

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

$\frac{256}{2^{15} \cdot 2^{2 \cdot 3}}$

Step 4.4.2

Multiply $2$ by $3$ .

$\frac{256}{2^{15} \cdot 2^{6}}$

Step 4.5

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

$\frac{256}{2^{15 + 6}}$

Step 4.6

Add $15$ and $6$ .

$\frac{256}{2^{21}}$

Step 5

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 5.1

Raise $2$ to the power of $21$ .

$\frac{256}{2097152}$

Step 5.2

Cancel the common factor of $256$ and $2097152$ .

Tap for more steps...

Step 5.2.1

Factor $256$ out of $256$ .

$\frac{256 (1)}{2097152}$

Step 5.2.2

Cancel the common factors.

Tap for more steps...

Step 5.2.2.1

Factor $256$ out of $2097152$ .

$\frac{256 \cdot 1}{256 \cdot 8192}$

Step 5.2.2.2

Cancel the common factor.

$\frac{256 \cdot 1}{256 \cdot 8192}$

Step 5.2.2.3

Rewrite the expression.

$\frac{1}{8192}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8192}$

Decimal Form:

$0.00012207 \dots$