Question

Which expression is equivalent to the expression shown: 10^4 * 4^10 / 4^5?

a) 10^4
b) 4^5
c) 4^10
d) 10^6

Answer 1

The expression 10^4 \* 4^10 / 4^5 simplifies to 10^4 \* 4^5 by subtracting the exponents of the same base during division, which does not match any of the provided answer choices.

The correct answer is A.

Step-by-step explanation:

The question asks to find an expression equivalent to 10^4 \* 4^10 / 4^5. We can simplify this expression by using the laws of exponents. We start by reducing the 4^10 / 4^5 part. Since we are dividing powers with the same base, we subtract the exponents, which gives us 4^(10-5) = 4^5. Thus, the expression simplifies to 10^4 \* 4^5.

The only multiplication in the expression is between different bases, so it cannot be further simplified to a single power. Therefore, the original expression is equivalent to the simplified form 10^4 \* 4^5, which does not match any of the given answer choices (a) 10^4, (b) 4^5, (c) 4^10, or (d) 10^6.