Question

Which expression is equivalent to 128x⁵⁸V ²x²y⁵? Assume x > 0 and y > 0.

A) 64x⁶⁰y⁵
B) 256x⁶⁰y⁵
C) 128x⁶⁰y⁵
D) 64x⁵⁸y⁵

Answer 1

The equivalent expression to the multiplication of 128x⁵⁸y² and 2x²y⁵, given that both x and y are greater than 0, is 256x⁶⁰y⁵, which corresponds to Option B.

Step-by-step explanation:

The question asks which expression is equivalent to 128x⁵⁸y² multiplied by 2x²y⁵ given that x and y are greater than 0. To find the equivalent expression, we follow the rules for multiplying expressions with exponents.

First, we multiply the coefficients (numbers in front of the variables): 128 times 2 equals 256.

Next, we apply the power rule for exponents for variables with the same base. When multiplying, we add the exponents of like bases:

• For x, we add the exponents 58 and 2 to get x raised to the power of 60 (x⁵⁸ × x² = x⁵⁸+2 = x⁶⁰).
• For y, since y² and y⁵ have different powers but the same base, we simply carry over the exponent from the term with the highest power, which is y⁵.

Thus, the product of 128x⁵⁸y² and 2x²y⁵ is 256x⁶⁰y⁵.

Therefore, the answer is Option B: 256x⁶⁰y⁵.