Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 x 5^−2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
To apply the properties of integer exponents and generate equivalent expressions with positive exponents, we can use the following rules:
1. For any nonzero number a, a^0 = 1.
2. For any nonzero number a, a^(-b) = 1/a^b.
3. For any nonzero number a, (a^b)/(a^c) = a^(b-c).
Using these rules, we can rewrite the expression 4^0 x 5^(-2)/(-2)^(-3) with positive exponents:
4^0 x 5^(-2)/(-2)^(-3) = 1 x 1/5^2 x (-1/2)^(-3)
= 1/5^2 x (-1/2)^(-3)
Next, we simplify the expression further using the negative exponent rule:
1/5^2 x (-1/2)^(-3) = 1/5^2 x (2/1)^3
= 1/5^2 x 2^3
= 1/25 x 8
Finally, we simplify the expression by multiplying 1/25 and 8:
1/25 x 8 = 8/25
Therefore, the simplified fraction with no remaining exponents is 8/25.
thats incorrect try again
Apologies for the mistake. Let's reassess the problem.
Using the properties of integer exponents:
1. Any number raised to the power of 0 is equal to 1.
Therefore, 4^0 = 1.
2. When a number with a negative exponent is in the denominator, we can move it to the numerator and change the sign of the exponent.
Therefore, 5^(-2) = 1/5^2.
3. Similarly, for (-2)^(-3), we can rewrite it as 1/(-2)^3.
Applying these properties, the expression 4^0 x 5^(-2) / (-2)^(-3) can be rewritten as:
1 x (1/5^2) / (1/(-2)^3)
= 1 x (1/25) / (1/(-8))
= 1 x (1/25) x (-8/1)
= -8/25
Therefore, the simplified fraction with no remaining exponents is -8/25.