Dividing Monomials

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.

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify 54y^10 ÷ 6y^5?

Back

To simplify, divide the coefficients (54 ÷ 6 = 9) and subtract the exponents of y (10 - 5 = 5), resulting in 9y^5.

Front

What does it mean to rewrite an expression using a positive exponent?

Back

Rewriting an expression using a positive exponent involves converting negative exponents to positive by taking the reciprocal of the base.

Front

Simplify (45x^6y^9) / (5x^4y^2). What is the result?

Back

The result is 9x^2y^7.

Front

What is the product of two monomials?

Back

The product of two monomials is found by multiplying their coefficients and adding their exponents for like bases.

Front

How do you simplify (2a^2b^4z)(6a^3b^2z^5)?

Back

Multiply the coefficients (2 * 6 = 12) and add the exponents for like bases: a^(2+3), b^(4+2), z^(1+5), resulting in 12a^5b^6z^6.

Front

What is a negative exponent?

Back

A negative exponent indicates that the base is on the opposite side of the fraction: a^(-n) = 1/a^n.

Front

How do you evaluate x^13 ÷ x^8?

Back

Using the quotient rule, subtract the exponents: x^(13-8) = x^5.

Front

What is the simplified form of 9y^5?

Back

9y^5 is already in its simplest form.