(-5d^-3)/(-4(d^-5)^3)
To simplify this expression, we will first rewrite it using positive exponents.
(-5/d^3)/(-4/d^15)^3
Now, let's simplify the expression step by step:
(-5/d^3) = -5d^(-3)
(-4/d^15)^3 = (-4)^3 / (d^15)^3 = -64 / d^45
So, now we have:
(-5d^(-3))/(-64/d^45)
To divide fractions, we multiply by the reciprocal of the denominator:
=(-5d^(-3)) * (-d^45/64)
=(-5 / 64) * (d^(-3) * d^45)
=(-5 / 64) * d^(45-3)
=(-5 / 64) * d^42
Therefore, the simplified expression is:
-5d^42 / 64
are you sure
I apologize for the mistake in my previous response. Let's correct the calculation:
Given expression: (-5d^-3)/(-4(d^-5)^3)
First, simplify the expression inside the parentheses:
(d^-5)^3 = d^(-5*3) = d^-15
Now, substitute back into the expression:
(-5d^-3)/(-4d^-15)
To simplify the division of terms with the same base:
d^(m)/d^(n) = d^(m-n)
Therefore:
-5d^(-3-15) / -4
-5d^-18 / -4
Now simplify the negative exponent:
-5 / d^18 * -4
= 20 / d^18
So, the correct simplified expression is 20/d^18