Do you know your exponents?

Using the Rules of Exponents :

$2^3 + 2^3 + 3^4 + 3^4 + 3^4$

$=2^3(1+1) + 3^4(1+1+1)$

$=2^3(2) + 3^4(3)$

$=\boxed{2^4 + 3^5}$

2³ is being added twice so it is multiplied by 2, therefore it is 2³×2=2^4. And 3^4 is being addedthree times so it is multiplied by 3, therefore 3^4×3=3^5. So the answer is 2^4+3^5

$(2^3 + 2^3) + (3^4 + 3^4 +3^4)$ . There are 2 $2^3$ 's so they can be rewritten as $2(2^3)$ . There are 3 $3^4$ so they can be rewritten as $3(3^4)$ . Because the 2 in front of $2(2^3)$ has the same base as the $2^3)$ on the inside, the exponents can be added (the 2 has an implied $2^1$ ). The same can be done for the 3 in front of the $3(3^4)$ which has an implied $3^1$ . This means that the $2(2^3)$ simplifies to $2^4$ and the $3(3^4)$ becomes $3^5$ . Now the addition of these two is $2^4 + 3^5$ .

the given value's sum is 259 and only option (a) satisfies it

(2^3+2^3)+(3^4+3^4+3^4) =2.2.2.(1+1)+3.3.3.3.(1+1+1) =2.2.2.2 + 3.3.3.3.3 =2^4 + 3^5

2^3 + 2^3 +3^4 +3^4 +3^4

=2^3 x 2 + 3^4 x 3

=2^4 +3^5........................................[2=2^1 and 3=3^1]

$2^3 + 2^3 + 3^4 + 3^4 + 3^4$

$=2^3(1+1) + 3^4(1+1+1)$

$=2^3(2) + 3^4(3)$

$=\boxed{2^4 + 3^5}$

$2^3+2^3+3^4+3^4+3^4=2^3(1+1)+3^4(1+1+1)=2^3 \times 2+3^4 \times 3=2^{3+1}+3^{4+1}=\boxed{\large{2^4+3^5}}$

2³*2 = 2³ + 2³ = 2²+² ||| 3²+² *3 = 3²+² + 3²+² + 3²+²

$2^3+2^3+3^4+3^4+3^4$

$=(2 \cdot 2^3)+(3 \cdot 3^4)$

$=\boxed{2^4+3^5}$

$2^3 + 2^3 + 3^4 + 3^4$

$= 2 \times 2^3 + 3 \times 3^4$

$= 2^4 + 3^5$

First, we can take 2^3, & 3^4 as a common value, i.e,

2^3 (1+1)+3^4 (1+1+1)

Afterwards, we can take it as,

2^3 (2)+3^4 (3)

Now, we know that when base is same, powers add up..so the result will be:

2^4+3^5

let 2^3=a,3^4=b =a+a+b+b+b=2a+3b =2(2^2)+3(3^4) =2^3+3^5(law of exponent:a^b*a=a^b+1 )

The sum is 2 times 2^3 and 3 times 3^4 = 2.2^3 + 3.3^4 = 2^(1+3) + 3^(1+4)= 2^4 + 3^5

2^3 + 2^3 + 3^4 + 3^4 + 3^4

= 2(2^3) + 3(3^4)

2 = 2^1 and 3 = 3^1

= 2^1 * 2^3 + 3^1 * 3^4

Product rule : a^n * a^m = a^(n+m)

Therefore:

2^1 * 2^3 = 2^4

And:

3^1 * 3^4 = 3^5

=2^4 + 3^5

2^3+2^3+3^4+3^4+3^4 =2.2^3+3.3^4 =2^4+3^5

2^3+2^3=2^3(1+1)

=2^3*2=2^4

3^4+3^4+3^4=3^4(1+1+1)

=3^4(3)

=3^5

2^4+3^5

this is one of the easiest problems to me for solving this kind of problems you must know how to take common. in this problem we will take 2^3 and 3^4 common