Question

Using exponential notation

Answer 1

Hello there!

Law of Exponent

$\displaystyle \large{ {a}^{ \frac{m}{n}} = \sqrt[n]{ {a}^{m} } }$

The first problem asks us to write the cube root of 17 in exponential form. Refer the exponent's law above.

$\displaystyle \large{ \sqrt[3]{17} = \sqrt[n]{ {a}^{m} } }$

Compare the terms.

• a = 17
• m = 1
• n = 3

Hence,

$\displaystyle \large{ \sqrt[3]{17} = {17}^{ \frac{1}{3} } }$

The second problem asks us to write 13^{1/2} in radical form. Refer the law above.

$\displaystyle \large{ {13}^{ \frac{1}{2} } = {a}^{ \frac{m}{n} } }$

Compare the terms.

• a = 13
• m = 1
• n = 2

Hence,

$\displaystyle \large{ {13}^{ \frac{1}{2} } = \sqrt{13} }$

Conclusion

• First answer is 17^{1/3}
• Second answer is √13

Let me know if you have any questions!

Topic: Exponent / Fractional Exponent and n-th root /