Algebra Examples

${(36 x)}^{\frac{1}{2}} {(49 x)}^{\frac{1}{2}}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $36 x$ .

$36^{\frac{1}{2}} x^{\frac{1}{2}} {(49 x)}^{\frac{1}{2}}$

Step 1.2

Rewrite $36$ as $6^{2}$ .

${(6^{2})}^{\frac{1}{2}} x^{\frac{1}{2}} {(49 x)}^{\frac{1}{2}}$

Step 1.3

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

$6^{2 (\frac{1}{2})} x^{\frac{1}{2}} {(49 x)}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$6^{2 (\frac{1}{2})} x^{\frac{1}{2}} {(49 x)}^{\frac{1}{2}}$

Step 2.2

Rewrite the expression.

$6^{1} x^{\frac{1}{2}} {(49 x)}^{\frac{1}{2}}$

Step 3

Simplify the expression.

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Step 3.1

Evaluate the exponent.

$6 x^{\frac{1}{2}} {(49 x)}^{\frac{1}{2}}$

Step 3.2

Apply the product rule to $49 x$ .

$6 x^{\frac{1}{2}} (49^{\frac{1}{2}} x^{\frac{1}{2}})$

Step 3.3

Rewrite using the commutative property of multiplication.

$6 \cdot 49^{\frac{1}{2}} x^{\frac{1}{2}} x^{\frac{1}{2}}$

Step 4

Multiply $x^{\frac{1}{2}}$ by $x^{\frac{1}{2}}$ by adding the exponents.

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Step 4.1

Move $x^{\frac{1}{2}}$ .

$6 \cdot 49^{\frac{1}{2}} (x^{\frac{1}{2}} x^{\frac{1}{2}})$

Step 4.2

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

$6 \cdot 49^{\frac{1}{2}} x^{\frac{1}{2} + \frac{1}{2}}$

Step 4.3

Combine the numerators over the common denominator.

$6 \cdot 49^{\frac{1}{2}} x^{\frac{1 + 1}{2}}$

Step 4.4

Add $1$ and $1$ .

$6 \cdot 49^{\frac{1}{2}} x^{\frac{2}{2}}$

Step 4.5

Divide $2$ by $2$ .

$6 \cdot 49^{\frac{1}{2}} x^{1}$

Step 5

Simplify the expression.

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Step 5.1

Simplify $6 \cdot 49^{\frac{1}{2}} x^{1}$ .

$6 \cdot 49^{\frac{1}{2}} x$

Step 5.2

Rewrite $49$ as $7^{2}$ .

$6 \cdot {(7^{2})}^{\frac{1}{2}} x$

Step 5.3

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

$6 \cdot 7^{2 (\frac{1}{2})} x$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

$6 \cdot 7^{2 (\frac{1}{2})} x$

Step 6.2

Rewrite the expression.

$6 \cdot 7^{1} x$

Step 7

Evaluate the exponent.

$6 \cdot 7 x$

Step 8

Multiply $6$ by $7$ .

$42 x$