If $a = 3$ and $b =-2$, find the values of:$a^a+ b^b$
Given:
$a = 3$ and $b =-2$
To do:
We have to find the value of $a^a+ b^b$.
Solution:
We know that,
$a^{-m}=\frac{1}{a^m}$
Therefore,
$a^a+ b^b=(3)^3+(-2)^{-2}$
$=27+\frac{1}{(-2^{2})}$
$=27+\frac{1}{4}$
$=\frac{27\times4+1}{4}$
$=\frac{108+1}{4}$
$=\frac{109}{4}$
Hence, $a^a+b^b=\frac{109}{4}$.
Related Articles
- If $a = 3$ and $b =-2$, find the values of:$a^b + b^a$
- If $a = 3$ and $b =-2$, find the values of:$(a+b)^{ab}$
- Find the value of \( a^{3}+b^{3}+3 a b^{2}+3 a^{2} b \) if \( a=2, b=-3 \).
- If \( a=2 \) and \( b=3 \), find the value of\( a+b \)\( a^{2}+a b \)\( 2 a-3 b \)\( 5 a^{2}-2 a b \)
- If \( x-\sqrt{3} \) is a factor of the polynomial \( a x^{2}+b x-3 \) and \( a+b=2-\sqrt{3} \). Find the values of \( a \) and \( b \).
- Simplify the expression and find its values if $a=-1, b=-3$.$4 a^{2}-b^{2}+6 a^{2}-7 b^{2}$
- If \( a+b=5 \) and \( a b=2 \), find the value of(a) \( (a+b)^{2} \)(b) \( a^{2}+b^{2} \)
- If \( a+b=5 \) and \( a b=2 \), find the value of(a) \( (a+b)^{2} \)(b) \( a^{2}+b^{2} \)(c) \( (a-b)^{2} \)
- If $a + b + c = 9$, and $a^2 + b^2 + c^2 = 35$, find the value of $a^3 + b^3 + c^3 - 3abc$.
- If \( x+1 \) is a factor of \( 2 x^{3}+a x^{2}+2 b x+1 \), then find the values of \( a \) and \( b \) given that \( 2 a-3 b=4 \).
- If a = 5 and b = $-$2 then the find the value of:(a $-$ b)2 $-$ (a $+$ b)2
- If \( a=2, b=3 \) and \( c=4, \) then find the value of \( 3 a-b+c \).
- If a=3 and b=-1then find the value of$5 ab-2 a^{2}+5 b^{2}$
- If the points $A( -2,\ 1) ,\ B( a,\ b)$ and $C( 4,\ -1)$ are collinear and $a-b=1$, find the values of $a$ and $b$.
- Find acute angles \( A \) and \( B \), if \( \sin (A+2 B)=\frac{\sqrt{3}}{2} \) and \( \cos (A+4 B)=0, A>B \).
Kickstart Your Career
Get certified by completing the course
Get Started