Simplify.
(2b^-4 c^6)^5
I get
b^20/32c^30
Is that right?
Write your answer using only positive exponents.
(2b^-4 c^6)^5 = 32c^(30)/(b^(20))
To simplify the expression (2b^(-4)c^6)^5, you need to apply the power rule, which states that when you raise a power to another power, you multiply the exponents.
Let's break down the expression step by step:
(2b^(-4)c^6)^5
First, let's simplify the base:
2^5 = 32
Now let's simplify the exponents:
b^(-4)^5 = b^(-4*5) = b^(-20)
c^6^5 = c^(6*5) = c^30
Finally, put the simplified base and exponents together:
32b^(-20)c^30
To write the answer using only positive exponents, we can use the rule that a negative exponent is equivalent to its reciprocal with a positive exponent. For example, b^(-20) is equal to 1/b^20.
So, the answer in positive exponent form is:
32c^30/b^20