Simplify (6^(1/4))(6^(1/4))(6^(1/4))*(6^(1/4))

$(6^{\frac{1}{4}}) \cdot (6^{\frac{1}{4}}) \cdot (6^{\frac{1}{4}}) \cdot (6^{\frac{1}{4}})$

Step 1

Multiply $6^{\frac{1}{4}}$ by $6^{\frac{1}{4}}$ by adding the exponents.

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

$6^{\frac{1}{4} + \frac{1}{4}} \cdot 6^{\frac{1}{4}} \cdot 6^{\frac{1}{4}}$

Combine the numerators over the common denominator.

$6^{\frac{1 + 1}{4}} \cdot 6^{\frac{1}{4}} \cdot 6^{\frac{1}{4}}$

Add $1$ and $1$ .

$6^{\frac{2}{4}} \cdot 6^{\frac{1}{4}} \cdot 6^{\frac{1}{4}}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$6^{\frac{2 \cdot 1}{2 \cdot 2}} \cdot 6^{\frac{1}{4}} \cdot 6^{\frac{1}{4}}$

Cancel the common factor.

$6^{\frac{2 \cdot 1}{2 \cdot 2}} \cdot 6^{\frac{1}{4}} \cdot 6^{\frac{1}{4}}$

Rewrite the expression.

$6^{\frac{1}{2}} \cdot 6^{\frac{1}{4}} \cdot 6^{\frac{1}{4}}$

Step 2

Multiply $6^{\frac{1}{2}}$ by $6^{\frac{1}{4}}$ by adding the exponents.

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

$6^{\frac{1}{2} + \frac{1}{4}} \cdot 6^{\frac{1}{4}}$

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

$6^{\frac{1}{2} \cdot \frac{2}{2} + \frac{1}{4}} \cdot 6^{\frac{1}{4}}$

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

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

$6^{\frac{2}{2 \cdot 2} + \frac{1}{4}} \cdot 6^{\frac{1}{4}}$

Multiply $2$ by $2$ .

$6^{\frac{2}{4} + \frac{1}{4}} \cdot 6^{\frac{1}{4}}$

Combine the numerators over the common denominator.

$6^{\frac{2 + 1}{4}} \cdot 6^{\frac{1}{4}}$

Add $2$ and $1$ .

$6^{\frac{3}{4}} \cdot 6^{\frac{1}{4}}$

Step 3

Multiply $6^{\frac{3}{4}}$ by $6^{\frac{1}{4}}$ by adding the exponents.

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

$6^{\frac{3}{4} + \frac{1}{4}}$

Combine the numerators over the common denominator.

$6^{\frac{3 + 1}{4}}$

Add $3$ and $1$ .

$6^{\frac{4}{4}}$

Divide $4$ by $4$ .

$6^{1}$

Step 4

Simplify $6^{1}$ .

$6$

Simplify (6^(1/4))*(6^(1/4))*(6^(1/4))*(6^(1/4))

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Simplify (6^(1/4))(6^(1/4))(6^(1/4))*(6^(1/4))