Linear Algebra Examples

$x \cdot x = y \cdot y \cdot y$

Step 1

Rewrite the equation as $y \cdot y \cdot y = x \cdot x$ .

$y \cdot y \cdot y = x \cdot x$

Step 2

Simplify $y \cdot y \cdot y$ .

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Step 2.1

Multiply $y$ by $y$ .

$y^{2} y = x \cdot x$

Step 2.2

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 2.2.1

Multiply $y^{2}$ by $y$ .

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Step 2.2.1.1

Raise $y$ to the power of $1$ .

$y^{2} y^{1} = x \cdot x$

Step 2.2.1.2

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

$y^{2 + 1} = x \cdot x$

Step 2.2.2

Add $2$ and $1$ .

$y^{3} = x \cdot x$

Step 3

Multiply $x$ by $x$ .

$y^{3} = x^{2}$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \sqrt[3]{x^{2}}$

Step 5

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 6