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# Equations with Cubic Roots Calculator

## Get detailed solutions to your math problems with our Equations with Cubic Roots step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of equations with cubic roots. This solution was automatically generated by our smart calculator:

$2\left(7b-1\right)^{\frac{1}{3}}=-4$

Removing the variable's exponent raising both sides of the equation to the power of $3$

$\left(2\sqrt[3]{7b-1}\right)^{\frac{1}{\frac{1}{3}}}={\left(-4\right)}^{\frac{1}{\frac{1}{3}}}$

Divide $1$ by $\frac{1}{3}$

$\left(2\sqrt[3]{7b-1}\right)^{3}={\left(-4\right)}^{\frac{1}{\frac{1}{3}}}$

Divide $1$ by $\frac{1}{3}$

$\left(2\sqrt[3]{7b-1}\right)^{3}={\left(-4\right)}^{3}$

Calculate the power ${\left(-4\right)}^{3}$

$\left(2\sqrt[3]{7b-1}\right)^{3}=-64$
2

Removing the variable's exponent raising both sides of the equation to the power of $3$

$\left(2\sqrt[3]{7b-1}\right)^{3}=-64$

The power of a product is equal to the product of it's factors raised to the same power

$2^{3}\left(\sqrt[3]{7b-1}\right)^{3}=-64$

Calculate the power $2^{3}$

$8\left(\sqrt[3]{7b-1}\right)^{3}=-64$

Simplify $\left(\sqrt[3]{7b-1}\right)^{3}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{3}$ and $n$ equals $3$

$8\left(7b-1\right)^{\frac{1}{3}\cdot 3}$

Multiply $\frac{1}{3}$ times $3$

$8\left(7b-1\right)$

Multiply $\frac{1}{3}$ times $3$

$8\left(7b-1\right)=-64$
3

The power of a product is equal to the product of it's factors raised to the same power

$8\left(7b-1\right)=-64$
4

Divide both sides of the equation by $8$

$\frac{8\left(7b-1\right)}{8}=-\frac{64}{8}$
5

Simplifying the quotients

$7b-1=-\frac{64}{8}$
6

Divide $-64$ by $8$

$7b-1=-8$
7

We need to isolate the dependent variable , we can do that by simultaneously subtracting $-1$ from both sides of the equation

$7b=-8-1\cdot -1$
8

Multiply $-1$ times $-1$

$7b=-8+1$
9

Subtract the values $1$ and $-8$

$7b=-7$
10

Divide both sides of the equation by $7$

$\frac{7b}{7}=-\frac{7}{7}$
11

Simplifying the quotients

$b=-\frac{7}{7}$
12

Divide $-7$ by $7$

$b=-1$

##  Final answer to the problem

$b=-1$

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