Algebra Examples

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

Step 1

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

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

Step 2

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

$\frac{1}{2^{- 1} \cdot 4^{2} \cdot 2^{2}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $2^{- 1}$ by $2^{2}$ by adding the exponents.

Tap for more steps...

Step 3.1.1

Move $2^{2}$ .

$\frac{1}{2^{2} \cdot 2^{- 1} \cdot 4^{2}}$

Step 3.1.2

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

$\frac{1}{2^{2 - 1} \cdot 4^{2}}$

Step 3.1.3

Subtract $1$ from $2$ .

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

Step 3.2

Simplify $2^{1} \cdot 4^{2}$ .

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

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

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

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

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$\frac{1}{2 \cdot 2^{2 \cdot 2}}$

Step 4.2.2

Multiply $2$ by $2$ .

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

Step 4.3

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

$\frac{1}{2^{1 + 4}}$

Step 4.4

Add $1$ and $4$ .

$\frac{1}{2^{5}}$

Step 5

Raise $2$ to the power of $5$ .

$\frac{1}{32}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{32}$

Decimal Form:

$0.03125$