Question

URGENT 25 POINTS!

Choose the expression that is equivalent to fraction with 8 raised to the negative tenth power in the numerator and 8 raised to the fourth power times 8 raised to the zero power in the denominator.


Group of answer choices


1 divided by 8 raised to the fourteenth power


814


negative 1 divided by 8 raised to the fourteenth power


−814

Answer 1

To find the equivalent expression, we can simplify the fraction by using the rule for exponents that says that when we divide two powers with the same base, we can subtract the exponents. Using this rule, we get:

(8^(-10)) / (8^4 * 8^0) = 8^(-10) / 8^4 = 8^(-10+4) = 8^(-6)

So the equivalent expression is: 1/8^6 = 8^(-6)

The correct answer is: 1 divided by 8 raised to the fourteenth power = 8^(-6)

Answer 2

To find the equivalent expression for the fraction 8^(-10)/8^4*8^0, we can use the property of exponents that states that any number raised to the power of 0 is equal to 1. Therefore, 8^0 is equal to 1.

Using the quotient rule of exponents, which states that when dividing two powers of the same base, we can subtract the exponents, we can simplify the expression to:

8^(-10)/8^4*8^0 = 8^(-10)/8^4 * 1 = 8^(-6).

Therefore, the equivalent expression to 8^(-10)/8^4*8^0 is 8^(-6). The correct answer is therefore 1 divided by 8 raised to the fourteenth power, or option A.