Algebra Examples

${(\frac{4^{\frac{5}{4}} \cdot {0.4}^{\frac{1}{4}}}{4^{\frac{1}{2}}})}^{\frac{1}{2}}$

Step 1

Raise $0.4$ to the power of $\frac{1}{4}$ .

${(\frac{4^{\frac{5}{4}} \cdot 0.79527072}{4^{\frac{1}{2}}})}^{\frac{1}{2}}$

Step 2

Multiply $4^{\frac{5}{4}}$ by $0.79527072$ .

${(\frac{4.4987306}{4^{\frac{1}{2}}})}^{\frac{1}{2}}$

Step 3

Simplify the denominator.

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Step 3.1

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

${(\frac{4.4987306}{{(2^{2})}^{\frac{1}{2}}})}^{\frac{1}{2}}$

Step 3.2

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

${(\frac{4.4987306}{2^{2 (\frac{1}{2})}})}^{\frac{1}{2}}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

${(\frac{4.4987306}{2^{2 (\frac{1}{2})}})}^{\frac{1}{2}}$

Step 3.3.2

Rewrite the expression.

${(\frac{4.4987306}{2^{1}})}^{\frac{1}{2}}$

Step 3.4

Evaluate the exponent.

${(\frac{4.4987306}{2})}^{\frac{1}{2}}$

Step 4

Divide $4.4987306$ by $2$ .

${2.2493653}^{\frac{1}{2}}$

Step 5

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{{2.2493653}^{1}}$

Step 6

Anything raised to $1$ is the base itself.

$\sqrt{2.2493653}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2.2493653}$

Decimal Form:

$1.49978841 \dots$