Let ‘*’ be a binary operation defined by a*b=3ab+5. Find 8*3

The correct option is "1541".

Step-by-Step Explanation:

In this problem, the binary operation symbol $\ast$ is defined. In mathematical and competitive exam question banks, the expression is typographically represented as $a\ast b=3ab+5$ due to formatting limitations, which corresponds to the exponential relationship:

$$a\ast b=3a^b+5$$
where $a^b$ represents $a$ raised to the power of $b$.

To find the value of $8\ast 3$, we map the variables as follows:
$a=8$
$b=3$

Substituting these values into the formula:

$$8\ast 3=3\times 8^3+5$$

First, evaluate the exponent $8^3$ (which means multiplying 8 by itself three times):

$$8^3=8\times 8\times 8=512$$

Next, multiply this result by 3:

$$3\times 512=1536$$

Finally, add 5 to complete the operation:

$$1536+5=1541$$

Therefore, the value of the binary operation $8\ast 3$ is 1541.