Question

math question please find the image below:

Answer 1

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 ___________.

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Answer

First, we need to find the LCM of 81.

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

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 $\bf 4^{12}$.

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