Algebra Examples

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

Step 1

Multiply ${(2 x)}^{x}$ by ${(2 x)}^{2 x}$ 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.

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

Step 1.2

Add $x$ and $2 x$ .

${({(2 x)}^{3 x})}^{\frac{1}{x}}$

Step 2

Apply the product rule to $2 x$ .

${(2^{3 x} x^{3 x})}^{\frac{1}{x}}$

Step 3

Apply the product rule to $2^{3 x} x^{3 x}$ .

${(2^{3 x})}^{\frac{1}{x}} {(x^{3 x})}^{\frac{1}{x}}$

Step 4

Multiply the exponents in ${(2^{3 x})}^{\frac{1}{x}}$ .

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Step 4.1

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

$2^{3 x \frac{1}{x}} {(x^{3 x})}^{\frac{1}{x}}$

Step 4.2

Cancel the common factor of $x$ .

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Step 4.2.1

Factor $x$ out of $3 x$ .

$2^{x \cdot 3 \frac{1}{x}} {(x^{3 x})}^{\frac{1}{x}}$

Step 4.2.2

Cancel the common factor.

$2^{x \cdot 3 \frac{1}{x}} {(x^{3 x})}^{\frac{1}{x}}$

Step 4.2.3

Rewrite the expression.

$2^{3} {(x^{3 x})}^{\frac{1}{x}}$

Step 5

Raise $2$ to the power of $3$ .

$8 {(x^{3 x})}^{\frac{1}{x}}$

Step 6

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

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Step 6.1

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

$8 x^{3 x \frac{1}{x}}$

Step 6.2

Cancel the common factor of $x$ .

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Step 6.2.1

Factor $x$ out of $3 x$ .

$8 x^{x \cdot 3 \frac{1}{x}}$

Step 6.2.2

Cancel the common factor.

$8 x^{x \cdot 3 \frac{1}{x}}$

Step 6.2.3

Rewrite the expression.

$8 x^{3}$