Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

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

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

Step 1.1.2

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

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Step 1.1.2.1

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

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

Step 1.1.2.2

Cancel the common factor of $2$ .

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Step 1.1.2.2.1

Cancel the common factor.

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

Step 1.1.2.2.2

Rewrite the expression.

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

Step 1.1.3

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

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

Step 1.1.4

Add $1$ and $1$ .

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

Step 1.2

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

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

Step 1.3

Simplify the denominator.

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Step 1.3.1

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

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

Step 1.3.2

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

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Step 1.3.2.1

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

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

Step 1.3.2.2

Cancel the common factor of $2$ .

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Step 1.3.2.2.1

Cancel the common factor.

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

Step 1.3.2.2.2

Rewrite the expression.

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

Step 1.3.3

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

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

Step 1.3.4

Add $1$ and $3$ .

$\frac{1}{4} - \frac{3}{2^{4}}$

Step 1.4

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

$\frac{1}{4} - \frac{3}{16}$

Step 2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{4} \cdot \frac{4}{4} - \frac{3}{16}$

Step 3

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{4}$ by $\frac{4}{4}$ .

$\frac{4}{4 \cdot 4} - \frac{3}{16}$

Step 3.2

Multiply $4$ by $4$ .

$\frac{4}{16} - \frac{3}{16}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 - 3}{16}$

Step 5

Subtract $3$ from $4$ .

$\frac{1}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{16}$

Decimal Form:

$0.0625$