Please simplify.

1.) (c^-3)^2d^4/d^-2=

2.)(e^4)^-3f^-5/f^-2=

3.)(8^-7/8)^-2=

thank you. :)

Just realize that a negative exponent switches the factor between numerator and denominator.

(c^-3)^2d^4/d^-2
= c^-6 d^4/d^-2
= d^6/c^6

(e^4)^-3f^-5/f^-2
= e^-12 f^-5/f^-2
= e^-12 f^-3
= 1/(e^12f^3)

(8^-7/8)^-2
= (8^-8)^-2
= 8^16

Thanks alot .

Sure! Let's simplify each expression step-by-step:

1.) (c^-3)^2d^4/d^-2

To simplify this expression, let's start with the exponentiation first. Square the base inside the parentheses, and then simplify the resulting expression:

(c^-3)^2 = c^(-3 * 2) = c^-6

Now, let's simplify the remaining terms:

d^4/d^-2 = d^(4 - (-2)) = d^6

Putting it all together, the simplified expression is:

c^-6 * d^6

2.) (e^4)^-3f^-5/f^-2

Again, let's start by simplifying the exponentiation:

(e^4)^-3 = e^(4 * -3) = e^-12

Now, let's simplify the remaining terms:

f^-5/f^-2 = f^(-5 - (-2)) = f^-3

Combining the simplified terms, the expression becomes:

e^-12 * f^-3

3.) (8^-7/8)^-2

To simplify this expression, let's start by evaluating the expression inside the parentheses:

8^-7/8 = 1/8^7 = 1/8^7

Since the numerator is 1, the expression remains the same:

(8^-7/8)^-2 = (1/8^7)^-2

Now, to simplify further, we can apply the power of a power rule. We need to distribute the exponent of -2 to both the numerator and the denominator:

(1/8^7)^-2 = 8^(7 * -2) = 8^-14

Therefore, the simplified expression is:

8^-14

I hope this helps! Let me know if you have any other questions.