Finite Math Examples

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

Step 1

Move ${(2^{- 2})}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Move ${(2^{3})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(2^{- 2})}^{2} {(2^{5})}^{- 3} {(2^{- 2})}^{4} {(2^{3})}^{2}}$

Step 3

Multiply ${(2^{- 2})}^{2}$ by ${(2^{- 2})}^{4}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move ${(2^{- 2})}^{4}$ .

$\frac{1}{{(2^{- 2})}^{4} {(2^{- 2})}^{2} {(2^{5})}^{- 3} {(2^{3})}^{2}}$

Step 3.2

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

$\frac{1}{{(2^{- 2})}^{4 + 2} {(2^{5})}^{- 3} {(2^{3})}^{2}}$

Step 3.3

Add $4$ and $2$ .

$\frac{1}{{(2^{- 2})}^{6} {(2^{5})}^{- 3} {(2^{3})}^{2}}$

Step 4

Move ${(2^{5})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(2^{5})}^{3}}{{(2^{- 2})}^{6} {(2^{3})}^{2}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

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

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

Step 5.1.2

Multiply $5$ by $3$ .

$\frac{2^{15}}{{(2^{- 2})}^{6} {(2^{3})}^{2}}$

Step 5.2

Raise $2$ to the power of $15$ .

$\frac{32768}{{(2^{- 2})}^{6} {(2^{3})}^{2}}$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

Multiply the exponents in ${(2^{- 2})}^{6}$ .

Tap for more steps...

Step 6.1.1

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

$\frac{32768}{2^{- 2 \cdot 6} {(2^{3})}^{2}}$

Step 6.1.2

Multiply $- 2$ by $6$ .

$\frac{32768}{2^{- 12} {(2^{3})}^{2}}$

Step 6.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{32768}{\frac{1}{2^{12}} {(2^{3})}^{2}}$

Step 6.3

Raise $2$ to the power of $12$ .

$\frac{32768}{\frac{1}{4096} {(2^{3})}^{2}}$

Step 6.4

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

Tap for more steps...

Step 6.4.1

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

$\frac{32768}{\frac{1}{4096} \cdot 2^{3 \cdot 2}}$

Step 6.4.2

Multiply $3$ by $2$ .

$\frac{32768}{\frac{1}{4096} \cdot 2^{6}}$

Step 6.5

Raise $2$ to the power of $6$ .

$\frac{32768}{\frac{1}{4096} \cdot 64}$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Combine $\frac{1}{4096}$ and $64$ .

$\frac{32768}{\frac{64}{4096}}$

Step 7.2

Cancel the common factor of $64$ and $4096$ .

Tap for more steps...

Step 7.2.1

Factor $64$ out of $64$ .

$\frac{32768}{\frac{64 (1)}{4096}}$

Step 7.2.2

Cancel the common factors.

Tap for more steps...

Step 7.2.2.1

Factor $64$ out of $4096$ .

$\frac{32768}{\frac{64 \cdot 1}{64 \cdot 64}}$

Step 7.2.2.2

Cancel the common factor.

$\frac{32768}{\frac{64 \cdot 1}{64 \cdot 64}}$

Step 7.2.2.3

Rewrite the expression.

$\frac{32768}{\frac{1}{64}}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$32768 \cdot 64$

Step 9

Multiply $32768$ by $64$ .

$2097152$