4^0 x 5^-2/(-2)^-3
To simplify this expression, we can follow the order of operations (PEMDAS).
Step 1: Calculate any exponents
4^0 = 1 (Any number raised to the power of 0 is equal to 1).
(-2)^-3 = 1/(-2)^3 = 1/(-2 x -2 x -2) = 1/-8 = -1/8
Step 2: Calculate the division
5^-2 / -1/8 = 5^-2 x -8/1
Step 3: Calculate the multiplication
5^-2 x -8/1 = (-8 x 1)/(5^2 x 1)
Step 4: Calculate the remaining exponents and multiplication
(-8 x 1)/(5^2 x 1) = -8/25
Therefore, 4^0 x 5^-2 / (-2)^-3 = -8/25.
To simplify the expression 4^0 × 5^(-2) / (-2)^(-3), let's break it down step by step:
Step 1: Simplify exponents
Recall that any number raised to the power of 0 is equal to 1, so 4^0 = 1. Also, for negative exponents, you can rewrite them as the reciprocal of the positive exponent. Therefore, 5^(-2) can be rewritten as 1 / 5^2, and (-2)^(-3) can be rewritten as 1 / (-2)^3.
Now the expression becomes 1 × 1 / 5^2 / 1 / (-2)^3.
Step 2: Evaluate exponents
Simplify the exponents:
1 × 1 / 5^2 / 1 / (-2)^3 =
1 × 1 / 25 / 1 / (-8) =
1 / 25 / (-8).
Step 3: Simplify the division
To simplify the division of fractions, multiply the first fraction by the reciprocal of the second fraction:
1 / 25 × (-8) / 1 =
-8 / 25.
Therefore, 4^0 × 5^-2 / (-2)^-3 simplifies to -8 / 25.
To solve this expression, let's break it down step by step:
Step 1: Evaluate the powers:
4^0 = 1 (any number raised to the power of 0 is equal to 1)
5^-2 = 1/5^2 = 1/25 (negative exponent means reciprocal)
(-2)^-3 = 1/(-2)^3 = 1/(-8) = -1/8 (negative exponent means reciprocal)
So now our expression becomes:
1 x (1/25)/(-1/8)
Step 2: Simplify the expression further:
To divide by a fraction, we multiply by its reciprocal, so:
(1/25) x (8/-1) = 8/(-25) = -8/25
Therefore, the value of 4^0 x 5^-2 / (-2)^-3 is -8/25.