Question

Simplify by using law of exponents 8⁻¹ x 2⁻³/10⁴

Answer 1

1/2500

Step-by-step explanation:

There are 3 parts: 8^-1, 2^-3, and 10^-4

The goal is to get as many of these exponents into the same number a in the form a^x. For this problem, we will try to convert most of these exponents into some form that includes the lowest number, 2.

for 8^-1, we can rewrite this as (2^3)^-1, which is equal to 2^-3

for 2^-3, we can leave as is.

for 10^-4, we can write this as 2^-4 * 5^-4

Now, let's evaluate the exponents with the bases of 2.

2^-3 * 2^-3/(2^4*5^4)

2^-6/2^4 * 1/5^4

2^-2 * 1/5^4

1/4 * 1/5^4

1/(4 * 5^4)

1/(4 * 625) = 1/2500

Hope this helps :)