Find the Product fourth root of 7* fourth root of 7* fourth root of 7* fourth root of 7

$\sqrt[4]{7} \cdot \sqrt[4]{7} \cdot \sqrt[4]{7} \cdot \sqrt[4]{7}$

Step 1

Multiply $\sqrt[4]{7}$ by $\sqrt[4]{7}$ .

${\sqrt[4]{7}}^{2} \cdot \sqrt[4]{7} \cdot \sqrt[4]{7}$

Step 2

Multiply ${\sqrt[4]{7}}^{2}$ by $\sqrt[4]{7}$ by adding the exponents.

Multiply ${\sqrt[4]{7}}^{2}$ by $\sqrt[4]{7}$ .

Raise $\sqrt[4]{7}$ to the power of $1$ .

${\sqrt[4]{7}}^{2} \cdot {\sqrt[4]{7}}^{1} \cdot \sqrt[4]{7}$

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

${\sqrt[4]{7}}^{2 + 1} \cdot \sqrt[4]{7}$

Add $2$ and $1$ .

${\sqrt[4]{7}}^{3} \cdot \sqrt[4]{7}$

Step 3

Multiply ${\sqrt[4]{7}}^{3}$ by $\sqrt[4]{7}$ by adding the exponents.

Multiply ${\sqrt[4]{7}}^{3}$ by $\sqrt[4]{7}$ .

Raise $\sqrt[4]{7}$ to the power of $1$ .

${\sqrt[4]{7}}^{3} \cdot {\sqrt[4]{7}}^{1}$

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

${\sqrt[4]{7}}^{3 + 1}$

Add $3$ and $1$ .

${\sqrt[4]{7}}^{4}$

Step 4

Rewrite ${\sqrt[4]{7}}^{4}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{7}$ as $7^{\frac{1}{4}}$ .

${(7^{\frac{1}{4}})}^{4}$

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

$7^{\frac{1}{4} \cdot 4}$

Combine $\frac{1}{4}$ and $4$ .

$7^{\frac{4}{4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$7^{\frac{4}{4}}$

Rewrite the expression.

$7^{1}$

Evaluate the exponent.

$7$