Question

√b⁹ / √b⁷ is equal to:
a) b
b) b²
c) b³
d) b^2

Answer 1

To simplify the expression √b⁹ / √b⁷, use the property of exponents and simplify to b.

Step-by-step explanation:

To simplify the expression √b⁹ / √b⁷, we can use the property of exponents that states x^(a-b) = x^a / x^b. Applying this property to the given expression, we have √b⁹ / √b⁷ = (b^9)^(1/2) / (b^7)^(1/2). Simplifying further, we get b^(9/2) / b^(7/2). Using the property that b^a / b^b = b^(a-b), we have b^(9/2 - 7/2), which simplifies to b^(2/2). And since 2/2 equals 1, the final answer is b^1, which is just b.

Answer 2

The expression √b⁹ / √b⁷ simplifies to b².(b)

Step-by-step explanation:

When you divide two square roots with the same base, you subtract the exponents. Here, √b⁹ divided by √b⁷ is simplified as √(b⁹ / b⁷) = √(b²) = b². The division of the exponents when working with square roots follows the property of exponents where when you divide terms with the same base, you subtract the exponents.(b)

In this case, √b⁹ divided by √b⁷ can be rewritten using the division property of exponents as √(b⁹ / b⁷), resulting in √(b²). Simplifying the square root of b² gives the final answer of b², as the square root of a squared term is simply the base value.