Question

( 5² x 5⁴) = _____ *


5²
5⁶
5⁸
25⁶​

Answer 1

Answer:

5^8 is right answer.

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Answer 2

Answer :-

• Option 3 is correct.

• 5² × 5⁴ = 5⁶.

To find :-

• 5² × 5⁴.

Step-by-step explanation :-

Detailed explanation of the solution :-

Let's understand!

In this question, we can see two numbers which have powers. So, first we are going to remove the powers by multiplication and at last, we will add the powers again in our answer, since all the options have powers. There are two methods for solving such problems. Let's see how we can solve this.

Calculations :-

Method 1)

This is a hard and time consuming method, but it is accurate and the answer will be correct.

5² = 5 × 5.

5⁴ = 5 × 5 × 5 × 5.

Now, we find their product in this way.

(5 × 5) × (5 × 5 × 5 × 5) = 5⁶.

So, 5² × 5⁴ = 5⁶.

Method 2)

We can also use the laws of exponents and powers to find the answer.

One law is that :-

If a is any rational number and m, n are natural numbers, then $\sf{a}^{m} \times {a}^{n} = {a}^{m + n}.$

So, let's apply this law.

Here, 5 is the rational number and 2, 4 are natural numbers. So,

$\sf {5}^{2} \times {5}^{4} = {5}^{2 + 4} = {5}^{6}.$

So, 5⁶ is the answer.

The answer is same in both the methods, hence we can use both of them.