Solve for b b = cube root of 42* cube root of 42* cube root of 42

$b = \sqrt[3]{42} \cdot \sqrt[3]{42} \cdot \sqrt[3]{42}$

Step 1

Multiply $\sqrt[3]{42}$ by $\sqrt[3]{42}$ .

$b = {\sqrt[3]{42}}^{2} \cdot \sqrt[3]{42}$

Step 2

Multiply ${\sqrt[3]{42}}^{2}$ by $\sqrt[3]{42}$ by adding the exponents.

Multiply ${\sqrt[3]{42}}^{2}$ by $\sqrt[3]{42}$ .

Raise $\sqrt[3]{42}$ to the power of $1$ .

$b = {\sqrt[3]{42}}^{2} \cdot {\sqrt[3]{42}}^{1}$

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

$b = {\sqrt[3]{42}}^{2 + 1}$

Add $2$ and $1$ .

$b = {\sqrt[3]{42}}^{3}$

Step 3

Rewrite ${\sqrt[3]{42}}^{3}$ as $42$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{42}$ as $42^{\frac{1}{3}}$ .

$b = {(42^{\frac{1}{3}})}^{3}$

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

$b = 42^{\frac{1}{3} \cdot 3}$

Combine $\frac{1}{3}$ and $3$ .

$b = 42^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$b = 42^{\frac{3}{3}}$

Rewrite the expression.

$b = 42^{1}$

Evaluate the exponent.

$b = 42$