Question

Which of the following is equivalent to the expression 4⁴ ×4 −6 ÷(4²)?

a) 1/(4¹⁰)
b) 1/(4²)
c) 4¹0
d) 4²

Answer 1

The expression 4⁴ ×4 −6 ÷(4²) is equivalent to b) 1/(4²).

Step-by-step explanation:

To simplify the expression, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). Let's break down the expression step by step:

4⁴ ×4 −6 ÷(4²)

First, evaluate the exponents:

256 × 4 - 6 ÷ 16

Next, perform multiplication and division:

1024 - 0.375

Finally, subtract:

1023.625

Now, rewrite the result as a fraction:

`\[ (1023.625)/(1) \]`

To simplify the fraction, we divide the numerator and denominator by 4:

`\[ (255.90625)/(0.25) \]`

Further, simplify by multiplying both the numerator and denominator by 4:

`\[ (1023.625)/(1) \]`

Thus, the simplified expression is 1/(4²), which is equivalent to option b). The correct answer is b) 1/(4²).