Question

How do you simplify $15^2 \times 15^4$ ?

Answer 1

Hint: In order to the question, the given expression is related to the product rule of exponents. So, firstly we will discuss the steps to simplify the product rule of expression and then we will go for solving the given expression by following the steps.

Complete step-by-step solution:
Firstly, we are going to discuss the steps to simplify the product rule of exponents:
Step-1: Check whether the base of terms is similar or not of the given expression.
Step-2: If the bases are the same, we will add the exponents of the bases together.
Step-3: If the bases are different, we will keep the exponents separate.
Step-4: If an exponent is negative, be sure to include the negative when adding.
Now, we will solve for the given expression:-
Given expression: $15^2 \times 15^4$
We can use here the rule of exponents to simplify the given expression-
$\therefore {x^a} \times {x^b} = {x^{a + b}}$
$
\Rightarrow {15^2} \times {15^4} \\
 \Rightarrow {15^{2 + 4}} \\
 \Rightarrow {15^6} \\
$

Hence, the simplified form of $15^2 \times 15^4$ is ${15^6}$.

Note: When raising an exponential expression to a power, we write the result with the common base and the product of the exponents. Be careful to distinguish between uses of the product rule and the power rule. When using the product rule, different terms with the same bases are raised to exponents. In this case, we can add the exponents.