Question

Part A: If (7^2)^x = 1, what is the value of x? Explain your answer. (10 points)

Part B: If (7^0)^x = 1, what are the possible values of x? Explain your answer. (15 points)

Answer 1

This is about understanding laws of indices.

A) x = 0

B) x = 1 or 0

Part A; (7²)ˣ = 1

• From Laws of indices, we know that any number raised to the power of 0 equals 1.

Thus; 7⁰ = 1

We now have;

(7²)ˣ = 7⁰

Opening the bracket, 2 will multiply x to give;

$7^{2x}$ = 7⁰

Both powers will be equal because their base numbers are equal.

Thus; 2x = 0

x = 0

Part B;

$(7^{0})^{x}$ = 1

Like in Part A, 7⁰ = 1

Thus;

1ˣ = 1⁰

Equating both powers; x = 0

Again, x could also be gotten from;

1ˣ = 1¹

x = 1

This is because 1¹ is still equal to 1.

x = 1 or 0

Read more at; https://brainly.com/question/6072736