Question

rewrite the given equation so there is a single power of 5,000 on each side. then, set the exponents equal to each other.

(1/5000)^2z · 5000^2z+2 = 5000

which equation shows the result?
a) 2=1
b) z=1
c) -4z+2=1
d) -4z+1=1

Answer 1

Answer:

Option a is correct.

$2 = 1$

Step-by-step explanation:

Using exponent rules:

$\frac{1}{a^n} = a^{-n}$

$a^n \cdot a^m = a^{n+m}$

Given the equation:

$(\frac{1}{5000})^{2z} \cdot (5000)^{2z+2} = 5000$

then;

$(5000)^{-2z} \cdot (5000)^{2z+2} = 5000$

Apply the exponent rules:

$(5000)^{-2z+2z+2} = 5000$

then;

$(5000)^{-2z+2z+2} = (5000)^1$

On comparing both sides we have;

$-2z+2z+2 = 1$

Combine like terms;

$2 = 1$

Therefore, the equation shows the result is, 2 = 1

Answer 2

When the same base with different exponents is multiplied together, then the result will be the addition of exponents, and when the same base with different exponents divides together then the result will be the subtraction of the exponents. If 2 = 1 then the given equation has a single power of 5,000 on each side.

The expression given in the question is,

$(1/5000)^{2z} \times 5000^{2z+2} = 5000$

We have to rewrite the given equation so there is a single power of 5,000 on each side.

The following are the identities or rules to follow while solving the powers.

$1/a^n=a^{-n}\\a^m/a^n=a^{m-n}\\a^m \times a^n=a^{m+n}$

Therefore, take the given expression to solve it further.

$(1/5000)^{2z} \times 5000^{2z+2} = 5000\\5000^{-2z} \times 5000^{2z+2}=5000\\5000^{-2z+2z+2}=5000^1$

Thus,

-2z+2z+2=1,

Hence, 2=1.

Option (a) is correct.

To know more about it, please refer to the link:

https://brainly.com/question/15993626