Question

Which of the following is equivalent to q/4³ * b⁻2/2⁴?

a) a/2¹0b²
b) a²/2¹0
c) a/2⁸b²
d) a/8⁷b²

Answer 1

The correct answer is a.a/2^10b^2, which is obtained by simplifying the original expression using the laws of exponents.

Step-by-step explanation:

The correct answer is option a/210b2. To find this, we simplify the given expression by the laws of exponents. Starting with q/43 × b-2/24, since the variables 'q' and 'a' do not appear together, we can assume there is a typo, and 'q' is meant to be 'a'.

Here's the step-by-step simplification:

1. Combine the fractions: (a/43) × (b-2/24) = a × b-2 / (43 × 24)
2. Simplify exponents: 43 = 26, thus we can combine the denominators: a × b-2 / (26 × 24)
3. Add the exponents of 2 in the denominator: a × b-2 / 26+4
4. Invert and multiply the b-2 to move to the numerator: a × b2 / 210 which is equivalent to the option a.

For q/4³, the exponent of 4 is 3, so we can rewrite it as q/(4^3) = q/64.

For b⁻²/2⁴, the exponent of 2 is 4 and the exponent of b is -2, so we can rewrite it as (b^(-2))/(2^4) = (1/b^2)/(16).

Multiplying q/64 by (1/b^2)/16, we get (q/64)*(1/b^2)/16 = (q/64)*(1/16)/(b^2) = q/(64*16*b^2).

Simplifying further, we get q/(64*16*b^2) = q/(1024*b^2).

Therefore, q/4³ * b⁻²/2⁴ is equivalent to a/2¹0b².