use the power rules for exponents to simply the expression (-5^7)^7
To simplify the expression (-5^7)^7 using the power rules for exponents, we need to apply the exponent to both the base and the exponent within the parentheses first.
First, let's simplify -5^7 within the parentheses:
-5^7 = -(5^7) [Since the negative sign is outside the parentheses, it applies to the entire term.]
Next, simplify the exponent of -5^7:
(-(5^7))^7 = (-5^7)^7 = (-5)^(7*7) [Applying the power rule for exponents, we multiply the exponents since the base (5) is the same.]
Finally, we simplify the exponent 7*7:
(-5)^(7*7) = (-5)^49
Therefore, the simplified expression is (-5)^49.