Question

Choose the expression that is equivalent to the quantity 8 raised to the negative second power times 8 raised to the fourth power end quantity all raised to the negative third power.

−86
1 divided by 8 raised to the sixth power
negative 1 divided by 8 raised to the sixth power
824
please help

Answer 1

To simplify the expression, we first simplify the exponents. Then, we multiply the bases with the same exponent. Finally, we raise the result to the negative exponent.

Step-by-step explanation:

To simplify the expression, we can use the rule for multiplying exponents when the bases are the same. In this case, we have 8 raised to the -2 power and 8 raised to the 4th power.

8 raised to the -2 power is 1 divided by 8 raised to the 2nd power, which is 1/64.

8 raised to the 4th power is 8 multiplied by itself 4 times, which is 4096.

So, (8 raised to the -2 power) multiplied by (8 raised to the 4th power) is equal to (1/64) multiplied by (4096), which simplifies to 64.

Finally, we raise 64 to the -3 power, which means we take the reciprocal of 64 raised to the 3rd power. The reciprocal of a number is 1 divided by that number.

So, 64 raised to the -3 power is equal to 1 divided by 64 raised to the 3rd power, which is 1 divided by 262144, or approximately 0.0000038147.