Algebra Examples

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

Step 1

Multiply $2^{\frac{1}{2}}$ by $2^{\frac{3}{4}}$ 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.

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Add $2$ and $3$ .

$(2^{\frac{5}{4}})$

Step 2

Remove parentheses.

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Step 2.1

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

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

Step 2.2

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

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

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 $\frac{2}{2}$ .

$2^{\frac{2}{2 \cdot 2} + \frac{3}{4}}$

Step 2.3.2

Multiply $2$ by $2$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Add $2$ and $3$ .

$2^{\frac{5}{4}}$

Step 3

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

$\sqrt[4]{2^{5}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt[4]{2^{5}}$

Decimal Form:

$2.37841423 \dots$