Simplify the following expression: $$\frac{(3x^4y^2)^2}{(3xy)^3}$$

$$\frac{9x^8y^4}{27x^3y^3} = \frac{1}{3}x^5y$$ .

How do you simplify $$\frac{(4a^2b^3)^3}{(2ab)^4}$$ ?

$$\frac{64a^6b^9}{16a^4b^4} = 4a^2b^5$$ .

What is the first step in dividing monomials?

The first step is to divide the coefficients (numerical parts) of the monomials.

What happens to the exponents when dividing monomials with different bases?

When dividing monomials with different bases, you cannot combine the exponents; you simplify each base separately.

Simplify $$\frac{(2x^3y^2)^2}{(4xy)^2}$$ .

$$\frac{4x^6y^4}{16x^2y^2} = \frac{1}{4}x^4y^2$$ .

What is the result of dividing a monomial by itself?

Dividing a monomial by itself results in 1, as long as the monomial is not zero.

How do you handle negative exponents when dividing monomials?

Negative exponents indicate the reciprocal; for example, $$a^{-n} = \frac{1}{a^n}$$ .

What is the simplified form of $$\frac{10x^4y^3}{5x^2y}$$ ?

$$2x^{4-2}y^{3-1} = 2x^2y^2$$ .

What is the significance of zero exponent in monomials?

Any non-zero base raised to the power of zero equals 1: $$a^0 = 1$$ .

Flashcard

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Mathematics

•

6th - 8th Grade

•

Practice Problem

•

Hard

•

CCSS

8.EE.A.1, HSA.APR.D.6, 6.EE.A.2B

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

What is 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 raised to non-negative integer powers.

FLASHCARD QUESTION

Front

What does it mean to divide monomials?

Back

Dividing monomials involves simplifying the expression by dividing the coefficients and subtracting the exponents of like bases.

Tags

CCSS.HSA.APR.D.6

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What is the rule for dividing powers with the same base?

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What is the coefficient in a monomial?

Back

Tags

CCSS.6.EE.A.2B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.A.1

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