Question

"Simplify the expression: 2^2 • 2 / 2⁻⁵ = 2^n. What is the value of n that makes this true?"

Select one:
a) 2
b) 5
c) 7
d) 9

Answer 1

To simplify the expression 2^2 • 2 / 2⁻⁵ = 2^n, we can first evaluate 2^2, which is equal to 4. Then, we can simplify 2 / 2⁻⁵ to 2 • 2⁵, which is 2 • 32 or 64. By rewriting 4 and 64 as powers of 2 and equating the exponents, we find that n = 8.

Step-by-step explanation:

To simplify the expression 2^2 • 2 / 2-5 = 2^n, we can start by evaluating 2^2, which is equal to 4. Next, we can simplify 2 / 2-5. When we divide by a negative exponent, it is the same as multiplying by the positive exponent. So, 2 / 2-5 becomes 2 • 25, which is equal to 2 • 32, or 64. Now, we have the equation 4 • 64 = 2^n. To solve for n, we can rewrite 4 and 64 as powers of 2, so the equation becomes 2^2 • 2^6 = 2^n. Using the rule of exponents that states when multiplying with the same base, we can add the exponents, we get 2^(2+6) = 2^n. Simplifying further, we have 2^8 = 2^n. Since the bases are equal, we can equate the exponents, so n = 8.