Simplify -3 fourth root of 64*(- fourth root of 8)

$- 3 \sqrt[4]{64} \cdot (- \sqrt[4]{8})$

Rewrite $64$ as $2^{4} \cdot 4$ .

Factor $16$ out of $64$ .

$- 3 \sqrt[4]{16 (4)} \cdot (- \sqrt[4]{8})$

Rewrite $16$ as $2^{4}$ .

$- 3 \sqrt[4]{2^{4} \cdot 4} \cdot (- \sqrt[4]{8})$

Pull terms out from under the radical.

$- 3 (2 \sqrt[4]{4}) \cdot (- \sqrt[4]{8})$

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

$- 3 (2 \sqrt[4]{2^{2}}) \cdot (- \sqrt[4]{8})$

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

$- 3 (2 \sqrt{\sqrt{2^{2}}}) \cdot (- \sqrt[4]{8})$

Pull terms out from under the radical, assuming positive real numbers.

$- 3 (2 \sqrt{2}) \cdot (- \sqrt[4]{8})$

Multiply $2$ by $- 3$ .

$- 6 \sqrt{2} \cdot (- \sqrt[4]{8})$

Multiply $- 6 \sqrt{2} (- \sqrt[4]{8})$ .

Multiply $- 1$ by $- 6$ .

$6 \sqrt{2} \sqrt[4]{8}$

Rewrite the expression using the least common index of $4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$6 (\sqrt[4]{8} \cdot 2^{\frac{1}{2}})$

Rewrite $2^{\frac{1}{2}}$ as $2^{\frac{2}{4}}$ .

$6 (\sqrt[4]{8} \cdot 2^{\frac{2}{4}})$

Rewrite $2^{\frac{2}{4}}$ as $\sqrt[4]{2^{2}}$ .

$6 (\sqrt[4]{8} \sqrt[4]{2^{2}})$

Combine using the product rule for radicals.

$6 \sqrt[4]{8 \cdot 2^{2}}$

Rewrite $8$ as $2^{3}$ .

$6 \sqrt[4]{2^{3} \cdot 2^{2}}$

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

$6 \sqrt[4]{2^{3 + 2}}$

Add $3$ and $2$ .

$6 \sqrt[4]{2^{5}}$

Raise $2$ to the power of $5$ .

$6 \sqrt[4]{32}$

Rewrite $32$ as $2^{4} \cdot 2$ .

Factor $16$ out of $32$ .

$6 \sqrt[4]{16 (2)}$

Rewrite $16$ as $2^{4}$ .

$6 \sqrt[4]{2^{4} \cdot 2}$

Pull terms out from under the radical.

$6 (2 \sqrt[4]{2})$

Multiply $2$ by $6$ .

$12 \sqrt[4]{2}$

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt[4]{2}$

Decimal Form:

$14.27048538 \dots$

Simplify -3 fourth root of 64*(- fourth root of 8)

Related Questions

Support LCMGCF.com by disabling your adblocker.