Question

Which expression is equivalent to 2⁴.7³.2.7⁻⁴ ?
a) 2¹¹
b) 2¹⁵
c) 7¹¹
d) 7¹⁵

Answer 1

After applying the laws of exponents, the expression simplifies to 2^5. This indicates a potential error in the provided options or the question, as 2^5 is not listed among the choices.

Step-by-step explanation:

To determine which expression is equivalent to 2⁴.7³.2.7⁻⁴, we can utilize the laws of exponents to simplify the expression:

First, let us combine like bases by adding the exponents:

• For the base 2: 2⁴ × 2 = 2⁴ × 2¹ = 2⁴+¹ = 2⁵
• For the base 7: 7³ × 7⁻⁴ = 7³-⁴ = 7⁻¹

Since 7⁻¹ is just 1/7, and any number divided by itself is 1, without changing the base 2 part, we can drop the 7 terms as 7³ × 7⁻⁴ is equal to 1:

This leaves us with just 2⁵, which is not one of the options given, suggesting a possible error in the options or in the question itself.