Which of the following represents the simplified form of the expression 4b^5 \cdot 2b^{-2}… — Armed Services Vocational Aptitude Battery (ASVAB)

Which of the following represents the simplified form of the expression $4b^5 \cdot 2b^{-2}$ ?

The simplified expression is

8b^3

The correct expression is found by multiplying the numerical coefficients (

4 \times 2 = 8

) and adding the exponents for the common base

b

(

5 + (-2) = 3

), resulting in

8b^3

Multiply the numerical coefficients.

4 \times 2 = 8

When multiplying algebraic terms, their numerical coefficients are multiplied together.

Apply the product rule of exponents to the variable terms.

b^5 \cdot b^{-2} = b^{5 + (-2)} = b^3

When multiplying exponential expressions with the same base, add their exponents.

Combine the coefficient and the variable term.

8b^3

This is the final simplified form of the expression.

When multiplying two exponential terms with the same base, multiply their coefficients and add their exponents.

Question