Algebra Examples

${(\sqrt{x})}^{6} \cdot {(\sqrt{x})}^{- 4}$

Step 1

Multiply ${(\sqrt{x})}^{6}$ by ${(\sqrt{x})}^{- 4}$ by adding the exponents.

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Step 1.1

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

${\sqrt{x}}^{6 - 4}$

Step 1.2

Subtract $4$ from $6$ .

${\sqrt{x}}^{2}$

Step 2

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 2.1

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

${(x^{\frac{1}{2}})}^{2}$

Step 2.2

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

$x^{\frac{1}{2} \cdot 2}$

Step 2.3

Combine $\frac{1}{2}$ and $2$ .

$x^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$x^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$x^{1}$

Step 2.5

Simplify.

$x$