Trigonometry Examples

${(1.892071)}^{3} = {(b^{\frac{1}{3}})}^{3}$

Step 1

Rewrite the equation as ${(b^{\frac{1}{3}})}^{3} = {1.892071}^{3}$ .

${(b^{\frac{1}{3}})}^{3} = {1.892071}^{3}$

Step 2

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$b^{\frac{1}{3}} = 1.892071$

Step 3

Solve for $b$ .

Tap for more steps...

Step 3.1

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(b^{\frac{1}{3}})}^{3} = {1.892071}^{3}$

Step 3.2

Simplify the exponent.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Simplify ${(b^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 3.2.1.1.1

Multiply the exponents in ${(b^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 3.2.1.1.1.1

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

$b^{\frac{1}{3} \cdot 3} = {1.892071}^{3}$

Step 3.2.1.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1.1.2.1

Cancel the common factor.

$b^{\frac{1}{3} \cdot 3} = {1.892071}^{3}$

Step 3.2.1.1.1.2.2

Rewrite the expression.

$b^{1} = {1.892071}^{3}$

Step 3.2.1.1.2

Simplify.

$b = {1.892071}^{3}$

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Raise $1.892071$ to the power of $3$ .

$b = 6.77348678$