Write the monomial in standard form: [tex]$9 y y^2 y$[/tex]
Answer (2)
Identify the monomial: 9 y y 2 y .
Rewrite the monomial using exponents: 9 ⋅ y 1 ⋅ y 2 ⋅ y 1 .
Add the exponents of the variable y : 1 + 2 + 1 = 4 .
Write the monomial in standard form: 9 y 4 .
Explanation
Understanding the Problem We are asked to write the monomial 9 y y 2 y in standard form. This means we need to simplify the expression by combining like terms and writing it with a single coefficient and variable raised to a power.
Applying Exponent Rules To simplify the monomial, we need to use the properties of exponents. Recall that when multiplying variables with the same base, we add their exponents. In this case, we have y , y 2 , and y . We can rewrite the monomial as 9 ⋅ y 1 ⋅ y 2 ⋅ y 1 .
Simplifying the Expression Now, we add the exponents of y : 1 + 2 + 1 = 4 . Therefore, the simplified monomial is 9 y 4 .
Final Answer The monomial in standard form is 9 y 4 .
Examples
Understanding monomials and their standard form is crucial in various fields. For instance, when calculating the area of a rectangle with sides 3 x and 3 x 3 , the area is 3 x ⋅ 3 x 3 = 9 x 4 . Simplifying monomials helps in determining areas, volumes, and other mathematical relationships in geometry and physics. This skill is also fundamental in polynomial arithmetic and algebraic manipulations.
The monomial 9 y y 2 y in standard form is 9 y 4 . To obtain this, we combined the exponents of y (1 + 2 + 1 = 4) and kept the coefficient at 9. Hence, the final expression is 9 y 4 .
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