use exponent rules to simplify. Write as a single power, don't need to find the value.
[ (11/20)^4 x (11/20)^-8]^5
and (11/20)^-6
you cant leave an number to the power of a negative exponent. You have to change it like this ex : 2^-3 = 1/2^3 = 1/8
[ (11/20)^4 x (11/20)^-8]^5
= [(11/20)^(4-8)]^5
= [(11/20)^-4]^5
= (11/20)^(-4*5)
= (11/20)^-20
= 1/(11/20)^20
= (20/11)^20
(11/20)^-6
= 1/(11/20)^6
= (20/11)^6
Thanks :)
Apply All Exponent Rules quick check answers?
To simplify the expression [ (11/20)^4 x (11/20)^-8 ]^5, we can apply the exponent rules.
First, let's deal with the exponents. According to the exponent rule, when you raise a power to another power, you multiply the exponents. So, we can multiply the exponents of the two terms inside the parentheses:
4 x -8 = -32.
Next, we apply the rule that a number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
Therefore, (11/20)^-8 can be rewritten as 1 / (11/20)^8.
Now, we have [ (11/20)^4 x 1 / (11/20)^8 ]^5.
We can simplify further by multiplying the two terms inside the parentheses. According to the rule, when you multiply two expressions with the same base, you add the exponents. So, we add 4 and -8:
(11/20)^4 x 1 / (11/20)^8 = (11/20)^(4 + -8) = (11/20)^-4
Now, we have [ (11/20)^-4 ]^5.
According to the rule, when you raise an expression to a power, you multiply the exponents. So, we multiply -4 and 5:
(11/20)^-4^5 = (11/20)^(-4 x 5) = (11/20)^-20.
Therefore, the expression [ (11/20)^4 x (11/20)^-8 ]^5 simplifies to (11/20)^-20.
Now let's simplify (11/20)^-6, as you mentioned.
To change a negative exponent to a positive exponent, we can use the rule that states a number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
So, (11/20)^-6 can be rewritten as 1 / (11/20)^6.
Thus, (11/20)^-6 simplifies to 1 / (11/20)^6.