Question

Tom simplified an expression in three steps, as shown: x to the power of negative 2 multiplied by y to the power of 4, over y multiplied by x to the power of 4 multiplied by x to the power of 4 multiplied by y to the power of negative 2, the whole to the power of 4 equal to x to the power of 2 multiplied by y to the power of 8, over y to the power of 4 multiplied by x to the power of 8 multiplied by x to the power of 8 multiplied by y to the power of 2 equal to x to the power of 2 multiplied by y to the power of 8, over y to the power of 6 multiplied by x to the power of 16. Which is the first incorrect step and why? (5 points) Step 1, all the exponents are increased by 4 Step 2, the exponents of the same base are added during multiplication Step 3, the exponents of the same base are subtracted during division Step 3, all the exponents are added during division

Answer 1

It would be number 3.

Explanation:

Answer 2

• Step 1, all the exponents are increased by 4

Explanation:

The three steps are

1. (x⁻² × y⁴ /y × x⁴ × x⁴ × y⁻²)⁴ =
2. x²×y⁸/y⁴×x⁸×x⁸×y² =
3. x²×y⁸/y⁶×x¹⁶

Correct solution should be:

• (x⁻² × y⁴ /y × x⁴ × x⁴ × y⁻²)⁴ = all powers inside the parenthesis should be multiplied by 4 as per power of the power (xᵃ)ᵇ = xᵃᵇ

This would give next steps:

1. x⁻⁸×y¹⁶/y⁴×x⁸×x⁸×y⁻⁸ =
2. x⁻⁸×y¹⁶/x¹⁶×y⁻⁴ =
3. y²⁰/x²⁴

Answer options:

Step 1, all the exponents are increased by 4

• There should be multiplication of powers. (It is close option but is not fully correct as not all the exponents increased by 4, for example y became y⁴)

Step 2, the exponents of the same base are added during multiplication

• It was done correctly

Step 3 wasn't performed yet, there was step 1 and 2.

• So answers about step 3 are irrelevant