Question
If $a=1, b=2$ then find the value of $\left(a^b+b^a\right)^{-1}$.
✓
Answer
Given, $a = 1$ and $b = 2$
$\therefore(\text{a}^{\text{b}}+\text{b}^{\text{a}})^{-1}$
$=\frac{1}{\text{a}^{\text{b}}+\text{b}^{\text{a}}}$
$=\frac{1}{1^2+2^1}$
$=\frac{1}{1+2}$
$=\frac{1}{3}$
$\therefore(\text{a}^{\text{b}}+\text{b}^{\text{a}})^{-1}$
$=\frac{1}{\text{a}^{\text{b}}+\text{b}^{\text{a}}}$
$=\frac{1}{1^2+2^1}$
$=\frac{1}{1+2}$
$=\frac{1}{3}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the surface area of a sphere of diameter $21\ cm.$
→Identify the polynomials in the following: $\text{g(x)}=2\text{x}^3-3\text{x}^2+\sqrt{\text{x}}-1$
→Determine the degree of the following polynomials. $-\frac{1}{2}\text{x}+3$
→In figure, $A, B, C, D$ are four points on the circle. $AC$ and $BD$ intersect at a point $E$ such that $\angle BEC = 130^\circ $ and $\angle ECD = 20^\circ $ Find $\angle BAC.$
→Find the zero of the polynomial in $p(x) = x – 5$
→Find the amount of water displaced by a solid spherical ball of diameter $0.21 m.$
→Find the volume of the right circular cone with radius $3.5$ and height $12\ cm$
→If $2^4 \times 4^2=16^x$, then find the value of $x$.
→Classify the following number as rational or irrational. give reasons to support your answer. $\sqrt{21}$
→Verify whether the following are True or False:
$-\frac{1}{3}$ is a zero of $3x + 1$
→$-\frac{1}{3}$ is a zero of $3x + 1$