monomials

Question 1

Is the following a Monomial? -5

Answer 1

Yes -5 is a real number and an example of a constant, or the product of -1*5

Question 2

Is the following a Monomial? p + q

Answer 2

No The expression involves the addition, not the product, of two variables

Question 3

Is the following a Monomial? x

Answer 3

Yes Single variables are monomials

Question 4

Is the following a Monomial? c / d

Answer 4

No The expression is the quotient, not the product, of two variables

Question 5

What is a monomial?

Answer 5

A monomial is a number, variable, or a product of a number and one or more variables.

Question 6

What is a constant?

Answer 6

A constant is a monomial that is a real number.

Question 7

How do you multiply monomials?

Answer 7

To multiply two powers that have the same base, add the exponents.

a⁴ * a¹² = a^{4 + 12} = a¹⁶

Question 8

Simplify the expression

(5x⁷)(x⁶)

Answer 8

(5x⁷)(x⁶) = (5)(1)(x⁷ * x⁶)

= (5 * 1)(x^{7 + 6})

= 5x¹³

Question 9

Simplify the Expression

(4ab⁶)(-7a²b³)

Answer 9

= (4 * -7)(a^{1 + 2})(b^{6 + 3})

= -28a³b⁹

(4ab⁶)(-7a²b³) = (4)(-7)(a * a²)(b⁶ * b³)

Question 10

How do you find the power of a power?

(4²)⁵

Answer 10

To find the power of a power Multiply the exponents.

(4²)⁵ = (4²)(4²)(4²)(4²)(4²)

= 4^{2 + 2 + 2 + 2 + 2}

= 4^{2 * 5}

= 4¹⁰

Question 11

Simplify

[(3²)³]²

Answer 11

[(3²)³]² = (3^{2 * 3})²

= (3⁶)²

= 3^{6 *2}

= 3¹²

Question 12

How do you find the power of a product?

(-2xy)³

Answer 12

To find the power of a product, find the power of each factor and multiply the exponents

(-2xy)³ = (-2)³x³y³

= -8x³y³

Question 13

To divide two powers that have the same base

b¹⁵ / b⁷

Answer 13

subtract the exponents

b¹⁵ / b⁷ = b^{15 - 7}

= b⁸

Question 14

Simplfy a⁵b⁸ / ab³

Answer 14

a⁵b⁸ / ab³ = (a⁵ / a)(b⁸ / b³)

= (a^{5 - 1})(b^{8 - 3})

= a⁴b⁵