express using positive exponents. simplify each. please
(-5c^-3)^4=?
thank you
Thank you thank you. (*^_^*)
-5c^-3 = -5/c^3
So,
(-5/c^3)^4 = 625/c^12
To express (-5c^-3)^4 using positive exponents, we need to apply the exponent rule which states that when we raise a power to another power, we need to multiply the exponents.
We will start by applying the exponent of 4 to each term within the parentheses, which results in:
((-5)^4) * (c^-3)^4
Now, let's simplify each term separately.
First, simplify (-5)^4:
(-5)^4 = (-5) * (-5) * (-5) * (-5) = 625
Now, let's simplify (c^-3)^4.
When raising a power to another power, we need to multiply the exponents. So, we have:
(c^-3)^4 = c^((-3) * 4) = c^-12
In this case, c^-12 means 1 over c^12.
So, putting it all together, we have:
(-5c^-3)^4 = 625 * (1/c^12) = 625/c^12
Therefore, the simplified expression is 625/c^12.