Fully simplify and write your answer in exponential form with positive exponents only
1/8^9 * 1/8^4 =
To fully simplify the expression 1/8^9 * 1/8^4, we can combine the bases (8) by adding their exponents:
1/8^9 * 1/8^4 = 1/8^(9+4)
Now, we can simplify the exponent:
1/8^(9+4) = 1/8^13
Therefore, the fully simplified expression, written in exponential form with positive exponents only, is 1/8^13.
z^-9 = 1/z^?
? =
We can solve for the missing exponent by noting that any number raised to the power of -1 is the reciprocal of that number.
So, if we have z^-9, to find the reciprocal, we need the exponent to be positive.
Therefore, ? = 9.
Thus, z^-9 = 1/z^9.
To fully simplify and write the expression in exponential form with positive exponents only, we can combine the two fractions and use the properties of exponents.
First, let's see how we can simplify the individual fractions:
1/8^9 can be written as (8^-9)
1/8^4 can be written as (8^-4)
Now, to combine the fractions, we multiply the numerators together and the denominators together:
(8^-9) * (8^-4) = 8^(-9-4)
Simplifying the exponent, we get:
(8^-9) * (8^-4) = 8^-13
Therefore, the fully simplified expression in exponential form with positive exponents only is 8^-13.
To simplify the given expression, we can use the rule of exponents which states that when you divide two exponential expressions with the same base, you subtract the exponents.
The given expression is:
1/8^9 * 1/8^4
To apply the exponent rule, we subtract the exponents:
1 / (8^9 * 8^4)
Now, we can use another exponent rule that says when you have a product of exponential expressions with the same base, you add the exponents:
1 / 8^(9 + 4)
Simplifying further, we add the exponents:
1 / 8^13
Finally, we can write the answer in exponential form with positive exponents:
1 / 8^13 = 8^(-13)