Algebra Examples

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

Step 1

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

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

Step 2

Multiply $4^{\frac{3}{4}}$ by $4^{- \frac{1}{2}}$ by adding the exponents.

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Step 2.1

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

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

Step 2.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

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

Step 2.3.2

Multiply $2$ by $2$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Subtract $2$ from $3$ .

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

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{1}{4^{\frac{1}{4}}}$ .

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

Step 3.2

One to any power is one.

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

Step 4

Simplify the denominator.

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Step 4.1

Multiply the exponents in ${(4^{\frac{1}{4}})}^{4}$ .

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Step 4.1.1

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

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

Step 4.1.2

Cancel the common factor of $4$ .

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Step 4.1.2.1

Cancel the common factor.

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

Step 4.1.2.2

Rewrite the expression.

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

Step 4.2

Evaluate the exponent.

$\frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$