Question

given: \\(\left(a^{3t}\
ight)\left(a^{10}\
ight)\\). for what value of \\(t\\) is the given expression equivalent to \\(a^{25}\\)?

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^{3t} \times a^{10} = a^{3t+10}$

Step2: Set exponents equal

Since the expressions are equivalent, their exponents are equal: $3t + 10 = 25$

Step3: Isolate the variable term

Subtract 10 from both sides: $3t = 25 - 10$
$3t = 15$

Step4: Solve for t

Divide both sides by 3: $t = \frac{15}{3}$

Answer:

$t = 5$