Which of the following is equivalent to the expression 8 to the -5 power times 8 to the second power

A) 1/8 to the 7 power
B) 1/8 to the 3 power
C) 8 to the 3 power
D) 8 to the 7 power
I was in between b and c but im pretty sure its c is it?

Nope. It's 8^-3, or 1/8^3

B

To solve this problem, we can use the property of exponents which states that when multiplying two powers with the same base, we add their exponents.

Given that 8^-5 x 8^2 is equivalent to (8^-5) x (8^2), we can add the exponents.

8^-5 represents 1/(8^5), and 8^2 represents 8^2. Therefore, the expression becomes 1/(8^5) x 8^2.

Simplifying further, 1/(8^5) x 8^2 is equal to 8^2/(8^5).

Using another exponent property, we subtract the exponents when dividing powers with the same base. So, 8^2/(8^5) is equal to 8^(2-5), which is equal to 8^-3.

Therefore, the answer is B) 1/8^3.

Please note that the other options are not correct because they do not follow the correct exponent rules.

To find the equivalent expression, you can combine the exponential terms with the same base by adding their exponents. In this case, you have 8 raised to the power of -5 multiplied by 8 raised to the power of 2.

Using the property of exponents, when multiplying two exponential terms with the same base, you add their exponents. Therefore, 8 to the -5 power times 8 to the 2nd power can be simplified as 8 to the (-5+2) power.

Now, simplify the exponent:
-5 + 2 = -3

So, the equivalent expression is 8 to the -3 power.

Now, let's look at the answer choices:
A) 1/8 to the 7 power: This is not the same as 8 to the -3 power.
B) 1/8 to the 3 power: This is also not the same as 8 to the -3 power.
C) 8 to the 3 power: This is not the same as 8 to the -3 power.
D) 8 to the 7 power: This is not the same as 8 to the -3 power.

None of the answer choices match the equivalent expression 8 to the -3 power. Therefore, neither B nor C is the correct answer.

It seems that none of the answer choices are equivalent to the given expression. Please double-check the question or consider asking for clarification.