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.