What is (i)(a*b^3)^7*(a/b)^{34} ?

The solution to (i)(a*b^3)^7*(a/b)^{34} is (a^{41})/(b^{13)}i

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simplify (i)(ab^3)^7(a/b)^{34}

simplify

(i) (a \cdot b^{3})^{7} \cdot (\frac{a}{b})^{34}

\frac{a ^{41}}{b ^{13}} i

Solution steps

(i) (a b^{3})^{7} (\frac{a}{b})^{34}

Apply rule:

(a) = a

(i) = i

= i (a b^{3})^{7} (\frac{a}{b})^{34}

Simplify

(a b^{3})^{7} : a^{7} b^{21}

= i a^{7} b^{21} (\frac{a}{b})^{34}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{a}{b})^{34} = \frac{a ^{34}}{b ^{34}}

= i a^{7} b^{21} \frac{a ^{34}}{b ^{34}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{a ^{7} b ^{21} a ^{34}}{b ^{34}} i

Cancel

\frac{a ^{7} b ^{21} a ^{34}}{b ^{34}} : \frac{a ^{41}}{b ^{13}}

= \frac{a ^{41}}{b ^{13}} i

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What is (i)(a*b^3)^7*(a/b)^{34} ?
The solution to (i)(a*b^3)^7*(a/b)^{34} is (a^{41})/(b^{13)}i