Finite Math Examples

$\sqrt{5 x - 1} P \sqrt{5 x - 1}$

Step 1

Multiply $\sqrt{5 x - 1} P \sqrt{5 x - 1}$ .

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Step 1.1

Raise $\sqrt{5 x - 1}$ to the power of $1$ .

$P ({\sqrt{5 x - 1}}^{1} \sqrt{5 x - 1})$

Step 1.2

Raise $\sqrt{5 x - 1}$ to the power of $1$ .

$P ({\sqrt{5 x - 1}}^{1} {\sqrt{5 x - 1}}^{1})$

Step 1.3

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

$P {\sqrt{5 x - 1}}^{1 + 1}$

Step 1.4

Add $1$ and $1$ .

$P {\sqrt{5 x - 1}}^{2}$

Step 2

Simplify terms.

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Step 2.1

Rewrite ${\sqrt{5 x - 1}}^{2}$ as $5 x - 1$ .

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Step 2.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x - 1}$ as ${(5 x - 1)}^{\frac{1}{2}}$ .

$P {({(5 x - 1)}^{\frac{1}{2}})}^{2}$

Step 2.1.2

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

$P {(5 x - 1)}^{\frac{1}{2} \cdot 2}$

Step 2.1.3

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

$P {(5 x - 1)}^{\frac{2}{2}}$

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Cancel the common factor.

$P {(5 x - 1)}^{\frac{2}{2}}$

Step 2.1.4.2

Rewrite the expression.

$P {(5 x - 1)}^{1}$

Step 2.1.5

Simplify.

$P (5 x - 1)$

Step 2.2

Apply the distributive property.

$P (5 x) + P \cdot - 1$

Step 2.3

Reorder.

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Step 2.3.1

Rewrite using the commutative property of multiplication.

$5 P x + P \cdot - 1$

Step 2.3.2

Move $- 1$ to the left of $P$ .

$5 P x - 1 \cdot P$

Step 3

Rewrite $- 1 P$ as $- P$ .

$5 P x - P$