Question

Help please i have no idea how to solve this

Answer 1

Answer: The answer is: "
`(1)/(80)` " .

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Explanation:

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Given: "
`{a^(3) = 5` " ; and: "
`b^(3) = 4` " ;

Find: "
`(ab^(2))^(-3)` " ;

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Note:

"
`(ab^2)^-^3 = a^-^3 b^(^2^*^-^3^) = a^-^3b^-^6 = (1)/(a^3) * (1)/(b^6)` ;

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Take note of the following properties of exponents:

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{Note: "
`(xy)^z = x^zy^z` ".

{Note: "
`(x^y)^z = x^(^y^*^z^)` ".

{Note: "
`x^(^-^y^) = (1)/(x^y)` " ; Assuming "
`x\\eq 0` " .}.

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We have: "
`(1)/(a^3)*(1)/(b^6)` " ;

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Given: "
`a^3 = 5` " ; We can substitute:

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"
`(1)/(a^3) = (1)/(5)` " ;

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Now, regarding: "
`b^6` " ;

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Given: "
`b^(3) = 4` " ;

Note that " 6 ÷ 3 = 2 " ;

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So: "
`b^(6) = (b^3)^2` " ; {since: "
`(a^m)^n = a^(^m^*^n^)` " } ;

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So: We can substitute "4" for "
`b^(3)` " ;

and solve for the value of: "
`b^(6)` " :

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"
`b^6 = (b^3)^2 = 4^2 = (4*4) = 16` " ;

So: "
`(1)/(b^6) = (1)/(16)` " ;

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Now, "
`(1)/(a^3)*(1)/(b^6)` =
`(1)/(5) * (1)/(16) = ((1*1))/((5*16)) = (1)/(80)` " .

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The answer is: "
`(1)/(80)` " .

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Hope this is helpful to you!

Wishing you the best!

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