Question

An expression is shown: (−7x¹²y⁻²z⁰)²(3y²z⁻¹). Which of the following is an equivalent algebraic expression?

a. −147xy⁸

b. 147xy⁸

c. −147xy⁻⁸

d. 147xy⁻²z⁻¹

Answer 1

To find the equivalent algebraic expression, we need to simplify the terms within the parentheses and then multiply them. The expression given is (−7x¹²y⁻²z⁰)²(3y²z⁻¹). The correct option is D.

Step-by-step explanation:

The expression given is (−7x¹²y⁻²z⁰)²(3y²z⁻¹). To find the equivalent algebraic expression, we need to simplify the terms within the parentheses and then multiply them.

First, square each term within the parentheses to get (49x²⁴y⁻⁴z⁰)(9y⁴z⁻¹).

Next, multiply the terms outside the parentheses together using the exponent rule for multiplication. Multiply the numbers: 49 x 9 = 441. Multiply the x terms and combine their exponents: 2⁴ x x¹² = x¹⁶. Multiply the y terms and combine their exponents: y⁻⁴ x y⁴ = y⁰ (which simplifies to 1). Multiply the z terms and combine their exponents: z⁰ x z⁻¹ = z⁻¹.

So, the equivalent algebraic expression is 441x¹⁶z⁻¹.