Question

$(5\sqrt{5})⁻²ˣ × 1 = \frac{1}{5} × 125ˣ⁻³$

A) $x = 2$
B) $x = 3$
C) $x = 1$
D) $x = 4$

Answer 1

To solve the equation, we simplify both sides using the rules of exponents. After simplification, we equate the exponents and solve for x, which is -1.

Step-by-step explanation:

To solve the equation, we can simplify both sides by applying the rules of exponents. On the left side, we have (5√5)-2x times 1, which is equal to 1 divided by (5√5)2x. On the right side, we have &#frac{1}{5} times 125x-3. Now let's simplify further:

1. On the left side, we can apply the rule (ab)c = abc to get 1 divided by (52)x times (51/2)2x. This becomes 1 divided by 52x times 5x.
2. On the right side, we have &#frac{1}{5} times (53)-x. This becomes &#frac{1}{5} times 5-

Now we can combine the terms on both sides:

1 divided by 52x times 5x = &#frac{1}{5} times 5-3

Since the bases are the same (5), we can equate the exponents:

2x + x = -3x

Combining like terms, we get 3x = -3x.Dividing both sides by 3, we get x = -1.

Therefore, the correct answer is x = -1.