Question

What is the value of ( 5^-2x10^-4)/(2^-5x5^-6) a. 0 b. 2 c. 5 d. 10

Answer 1

Answer:

2

Step-by-step explanation:

Answer 2

The value of ( 5^-2x10^-4)/(2^-5x5^-6) is 2 (option b).

Given,

( 5^-2x10^-4)/(2^-5x5^-6)

To find,

The value of ( 5^-2x10^-4)/(2^-5x5^-6).

Solution,

The value of ( 5^-2x10^-4)/(2^-5x5^-6) will be 2.

We can easily solve this problem using the basic concepts of base and exponents.

Now, we know that in the division the powers get subtracted and in multiplication, the powers are added given that the base is the same.

( 5^-2x10^-4)/(2^-5x5^-6)

Here, the base 5 is the same in the numerator and denominator.

So, the powers will get subtracted: 5^ -2-(-6).

It will be 5^(-2+6) that is 5^4.

Then, we have

5^4×10^-4/2^-5

We can write 10 as 2×5.

So,

5^4 × 2^-4 × 5^-4/2^-5

Adding the powers of 5^4 and 5^-4, we will have 5^0. Then, its value will be 1.

1×2^-4/2^-5

In division, the powers get subtracted. So,

2^-4-(-5)

2^(-4+5)

2^1

2

Hence, the value will be 2.