Question

What is a equivalent expression to 6(8x + 1), -35 + 30, 6(3y - 1/2), 1.6 + (2x + 0.4) , 8w - 16 , 2.2x + 2.2 , 100(z2(two is the exponet) - 5.38), 8 x y3 ( three is the exponet) x 3/4

Answer 1

Equivalent expressions are found by distributing constants, combining like terms, and applying exponent rules. For example, 6(8x + 1) becomes 48x + 6, and 8 x y^3 x 3/4 simplifies to 6y^3.

Step-by-step explanation:

The student's question involves finding equivalent expressions for a set of algebraic expressions. Simplifying algebraic expressions often involves distributing constants over addition or subtraction within parentheses, combining like terms, or applying the rules of exponents.

• For 6(8x + 1), we distribute the 6 to get 48x + 6.
• -35 + 30 combines to -5.
• For 6(3y - 1/2), distribute the 6 to get 18y - 3.
• Add together 1.6 + (2x + 0.4) to get 2x + 2.
• 8w - 16 can be factored to 8(w - 2).
• 2.2x + 2.2 has a common factor of 2.2, so it simplifies to 2.2(x + 1).
• The expression 100(z^2 - 5.38) is already in its simplest form.
• For 8 x y^3 x 3/4, multiply 8 by 3/4 and keep y^3 to get 6y^3.

When converting or manipulating exponents, we apply the appropriate arithmetic rules, such as adding exponents when multiplying terms and subtracting exponents when dividing terms with the same base.