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Sagot :
When multiplying numbers with the same base, we just add the exponents, and that will be the exponent of the product.
[tex]k^{2/5}*k^{6/7}=k^{2/5+6/7}=k^{44/35}= \sqrt[35]{k^{44}} [/tex]
[tex]k^{2/5}*k^{6/7}=k^{2/5+6/7}=k^{44/35}= \sqrt[35]{k^{44}} [/tex]
1) Change the fractional exponents to similar fractions. LCD of denominators 5 and 7 is 35.
2) Re-write as:
[tex](k ^{ \frac{14}{35} } ) (k ^{ \frac{30}{35} } )[/tex]
3) Multiply (add the exponents):
[tex](k ^{ \frac{14}{35} } ) (k ^{ \frac{30}{35} } ) = k ^{ \frac{44}{35} } [/tex]
4) As radical expression, the denominator is the nth root, the numerator is the exponent of the radicand k.
[tex]k ^{ \frac{44}{35} } = \sqrt[35]{k ^{44} } [/tex]
2) Re-write as:
[tex](k ^{ \frac{14}{35} } ) (k ^{ \frac{30}{35} } )[/tex]
3) Multiply (add the exponents):
[tex](k ^{ \frac{14}{35} } ) (k ^{ \frac{30}{35} } ) = k ^{ \frac{44}{35} } [/tex]
4) As radical expression, the denominator is the nth root, the numerator is the exponent of the radicand k.
[tex]k ^{ \frac{44}{35} } = \sqrt[35]{k ^{44} } [/tex]
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