Basic Math Examples

| \frac{{(\sqrt{\sqrt[6]{69}})}^{5} \cdot \frac{16}{11}}{3} |

$| \frac{{(\sqrt{\sqrt[6]{69}})}^{5} \cdot \frac{16}{11}}{3} |$

Step 1

Combine

{\sqrt{\sqrt[6]{69}}}^{5}

${\sqrt{\sqrt[6]{69}}}^{5}$ and

\frac{16}{11}

$\frac{16}{11}$ .

| \frac{\frac{{\sqrt{\sqrt[6]{69}}}^{5} \cdot 16}{11}}{3} |

$| \frac{\frac{{\sqrt{\sqrt[6]{69}}}^{5} \cdot 16}{11}}{3} |$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite

\sqrt{\sqrt[6]{69}}

$\sqrt{\sqrt[6]{69}}$ as

\sqrt[12]{69}

$\sqrt[12]{69}$ .

| \frac{\frac{{\sqrt[12]{69}}^{5} \cdot 16}{11}}{3} |

$| \frac{\frac{{\sqrt[12]{69}}^{5} \cdot 16}{11}}{3} |$

Step 2.2

Rewrite

{\sqrt[12]{69}}^{5}

${\sqrt[12]{69}}^{5}$ as

\sqrt[12]{69^{5}}

$\sqrt[12]{69^{5}}$ .

| \frac{\frac{\sqrt[12]{69^{5}} \cdot 16}{11}}{3} |

$| \frac{\frac{\sqrt[12]{69^{5}} \cdot 16}{11}}{3} |$

Step 2.3

Raise

69

$69$ to the power of

5

$5$ .

| \frac{\frac{\sqrt[12]{1564031349} \cdot 16}{11}}{3} |

$| \frac{\frac{\sqrt[12]{1564031349} \cdot 16}{11}}{3} |$

| \frac{\frac{\sqrt[12]{1564031349} \cdot 16}{11}}{3} |

$| \frac{\frac{\sqrt[12]{1564031349} \cdot 16}{11}}{3} |$

Step 3

Move

16

$16$ to the left of

\sqrt[12]{1564031349}

$\sqrt[12]{1564031349}$ .

| \frac{\frac{16 \sqrt[12]{1564031349}}{11}}{3} |

$| \frac{\frac{16 \sqrt[12]{1564031349}}{11}}{3} |$

Step 4

Multiply the numerator by the reciprocal of the denominator.

| \frac{16 \sqrt[12]{1564031349}}{11} \cdot \frac{1}{3} |

$| \frac{16 \sqrt[12]{1564031349}}{11} \cdot \frac{1}{3} |$

Step 5

Multiply

\frac{16 \sqrt[12]{1564031349}}{11} \cdot \frac{1}{3}

$\frac{16 \sqrt[12]{1564031349}}{11} \cdot \frac{1}{3}$ .

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Step 5.1

Multiply

\frac{16 \sqrt[12]{1564031349}}{11}

$\frac{16 \sqrt[12]{1564031349}}{11}$ by

\frac{1}{3}

$\frac{1}{3}$ .

| \frac{16 \sqrt[12]{1564031349}}{11 \cdot 3} |

$| \frac{16 \sqrt[12]{1564031349}}{11 \cdot 3} |$

Step 5.2

Multiply

11

$11$ by

3

$3$ .

| \frac{16 \sqrt[12]{1564031349}}{33} |

$| \frac{16 \sqrt[12]{1564031349}}{33} |$

| \frac{16 \sqrt[12]{1564031349}}{33} |

$| \frac{16 \sqrt[12]{1564031349}}{33} |$

Step 6

\frac{16 \sqrt[12]{1564031349}}{33}

$\frac{16 \sqrt[12]{1564031349}}{33}$ is approximately

2.83004384

$2.83004384$ which is positive so remove the absolute value

\frac{16 \sqrt[12]{1564031349}}{33}

$\frac{16 \sqrt[12]{1564031349}}{33}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{16 \sqrt[12]{1564031349}}{33}

$\frac{16 \sqrt[12]{1564031349}}{33}$

Decimal Form:

2.83004384 \dots

$2.83004384 \dots$