9.3 Monomials Power Rule Day 2

Front

What is the Power Rule for exponents?

Back

The Power Rule states that when raising a power to another power, you multiply the exponents. For example, \( (a^m)^n = a^{m \cdot n} \).

Front

Simplify the expression: \( (3u^2v^3)^2 \)

Back

\( 9u^4v^6 \) - Apply the Power Rule to each factor.

Front

What is the result of \( (3y^4)^2 \)?

Back

\( 9y^8 \) - Square the coefficient and multiply the exponents.

Front

How do you simplify \( (2x^3y)^6 \)?

Back

\( 64x^{18}y^6 \) - Distribute the exponent to each term: \( 2^6 = 64, (x^3)^6 = x^{18}, (y^1)^6 = y^6 \).

Front

What happens when you square a negative term, like \( (-5y^4)^2 \)?

Back

The result is positive: \( 25y^8 \) - Squaring a negative number results in a positive number.

Front

Define a monomial.

Back

A monomial is a polynomial with only one term, which can be a number, a variable, or a product of numbers and variables.

Front

What is the coefficient in the monomial \( 7x^3 \)?

Back

The coefficient is 7, which is the numerical factor in the term.

Front

How do you multiply monomials?

Back

Multiply the coefficients and add the exponents of like bases. For example, \( 3x^2 \cdot 4x^3 = 12x^{2+3} = 12x^5 \).

Front

What is the result of \( (xy^2)^3 \)?

Back

\( x^3y^6 \) - Apply the Power Rule to both variables.

Front

Explain the difference between a monomial and a polynomial.

Back

A monomial has one term, while a polynomial can have multiple terms (e.g., \( 3x^2 + 2x + 1 \)).