108k views
2 votes
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

User Giaour
by
8.0k points

1 Answer

5 votes

Final answer:

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.

User Deceze
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories