To apply the properties of integer exponents, we can rewrite the expression as follows:
4^0 ⋅ 5^(-2) / (-2)^(-3)
= 1 ⋅ 1 / ((-1)^3/2)^(-3)
= 1 / ((-1)^(3/2))^(-3)
Now, let's simplify the exponents:
(-1)^(3/2) = -1 * √(-1) = -1 * i = -i (since the square root of -1 is defined as i)
Now we have:
1 / (-i)^(-3)
= 1 / [(1/(-i))^3]
= 1 / (1/(-i^3))
= 1 / (1/i)
= 1 / (1/i) * (i/i)
= 1 / (i^2)
= 1 / (-1)
= -1
Therefore, the expression simplifies to -1.
v\Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 5^−2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
4^0 ⋅ 5^−2/(−2)^−3
1 answer