Finite Math Examples

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

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

Step 1

Multiply

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

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

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Step 1.1

Raise

\sqrt{5 x - 1}

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

1

$1$ .

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

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

Step 1.2

Raise

\sqrt{5 x - 1}

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

1

$1$ .

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

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 1.4

Add

1

$1$ and

1

$1$ .

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

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

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

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

Step 2

Simplify terms.

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Step 2.1

Rewrite

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

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

5 x - 1

$5 x - 1$ .

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Step 2.1.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{5 x - 1}

$\sqrt{5 x - 1}$ as

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

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

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

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 2.1.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

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

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

Step 2.1.4

Cancel the common factor of

2

$2$ .

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Step 2.1.4.1

Cancel the common factor.

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

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

Step 2.1.4.2

Rewrite the expression.

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

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

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

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

Step 2.1.5

Simplify.

P (5 x - 1)

$P (5 x - 1)$

P (5 x - 1)

$P (5 x - 1)$

Step 2.2

Apply the distributive property.

P (5 x) + P \cdot - 1

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

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

$5 P x + P \cdot - 1$

Step 2.3.2

Move

- 1

$- 1$ to the left of

P

$P$ .

5 P x - 1 \cdot P

$5 P x - 1 \cdot P$

5 P x - 1 \cdot P

$5 P x - 1 \cdot P$

5 P x - 1 \cdot P

$5 P x - 1 \cdot P$

Step 3

Rewrite

- 1 P

$- 1 P$ as

- P

$- P$ .

5 P x - P

$5 P x - P$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$