Question

Simplify each expression

-21v⁶/ -6v⁸, v≠0
A. 7/2v⁻²
B. 7/2v⁻²
C. 7/2 v²
D. 7/2v¹⁴

Answer 1

the final simplified form of the expression is 7/2v^(-2), which corresponds to option B.

Step-by-step explanation:

To simplify the expression -21v⁶ / -6v⁸, where v ≠ 0, we start by dividing the coefficients and subtracting the exponents of the same base according to the quotient rule for exponents. The quotient rule states that when dividing exponents with the same base, you subtract the exponents.

First step, divide the coefficients:

• -21 / -6 = 3.5 or 7/2

Second step, subtract the exponents of v:

• v⁶ / v⁸ = v^(6-8) = v^(-2)

Therefore, the simplified expression is 7/2v^(-2).

When the exponent is negative, it means that the term is the reciprocal of the base raised to the positive of that exponent:

• v^(-2) = 1 / v^2

Hence, the final simplified form of the expression is 7/2v^(-2), which corresponds to option B.