Math, asked by jimmygta5test, 7 months ago

math question please find the image below:

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Answered by spacelover123
3

Question

If 'a' and 'b' are positive integers such that a < b and \sf a^{b} =81 then the value of \sf b^{ab} is ___________.

\rule{300}{1}

Answer

First, we need to find the LCM of 81.

\begin{array}{r | l}  3&amp; 81\\ \cline{2-2}  3&amp;27  \\ \cline{2-2}  3&amp; 9 \\ \cline{2-2}  &amp; 3 \\ \end{array}

So, 81 = 3×3×3×3 = \sf 3^{4}

According to the question, 'a' is the base and 'b' is the exponent.

We also know that 'b' is greater than 'a'.

So if 81 =  \sf  3^{4}

Exponent is greater than base. So we know that the value of 'a' is 3 and the value of 'b' is 4.

Now we need to find the value of b^{ab}

Using the values we got we will substitute the values.

\sf  b^{ab} = 4^{3\times 4}

\sf 4^{12}

∴The answer is \bf  4^{12}.

\rule{300}{1}

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