Algebra Examples

$4^{- 6} \cdot 4^{4} \cdot {(2^{3} \cdot 2^{- 4})}^{- 1}$

Step 1

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

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Step 1.1

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

$4^{- 6 + 4} \cdot {(2^{3} \cdot 2^{- 4})}^{- 1}$

Step 1.2

Add $- 6$ and $4$ .

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

Step 2

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

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

Step 3

Raise $4$ to the power of $2$ .

$\frac{1}{16} \cdot {(2^{3} \cdot 2^{- 4})}^{- 1}$

Step 4

Multiply $2^{3}$ by $2^{- 4}$ by adding the exponents.

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Step 4.1

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

$\frac{1}{16} \cdot {(2^{3 - 4})}^{- 1}$

Step 4.2

Subtract $4$ from $3$ .

$\frac{1}{16} \cdot {(2^{- 1})}^{- 1}$

Step 5

Multiply the exponents in ${(2^{- 1})}^{- 1}$ .

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Step 5.1

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

$\frac{1}{16} \cdot 2^{- - 1}$

Step 5.2

Multiply $- 1$ by $- 1$ .

$\frac{1}{16} \cdot 2^{1}$

Step 6

Evaluate the exponent.

$\frac{1}{16} \cdot 2$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Factor $2$ out of $16$ .

$\frac{1}{2 (8)} \cdot 2$

Step 7.2

Cancel the common factor.

$\frac{1}{2 \cdot 8} \cdot 2$

Step 7.3

Rewrite the expression.

$\frac{1}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$