4 ^ 0 * 5 ^ - 2(- 2) ^ - 3
To solve this expression, we use the order of operations (also known as PEMDAS). Here's how we break it down step by step:
Step 1: Simplify the parentheses ().
(-2) ^ -3 = 1 / (-2)^3 = 1 / (-8) = -1/8
Step 2: Solve the exponentiation ^
4 ^ 0 * 5 ^ -2 * (-1/8)
Since any number to the power of 0 is always 1, the first term simplifies to 1.
1 * 5 ^ -2 * (-1/8)
Step 3: Simplify the exponents and multiply
5 ^ -2 = 1 / 5^2 = 1 / 25
(1 / 25) * (-1/8)
Step 4: Multiply the fractions
1 * -1 / 25 * 8 = -1/200
To simplify the expression 4 ^ 0 * 5 ^ -2 * (-2) ^ -3, follow the order of operations (PEMDAS) where you perform any calculations within parentheses first, then exponentiation, multiplication, and division from left to right.
Step 1: Evaluate the exponent (-2) ^ -3
Since the base (-2) is negative and the exponent is odd, the result will be negative. So, (-2) ^ -3 is equal to -1 / (-2) ^ 3.
Step 2: Evaluate (-2) ^ 3
Squaring the base (-2) gives 4, and multiplying it by the base (-2) again gives -8. So, (-2) ^ 3 is equal to -8.
Step 3: Calculate -1 / (-2) ^ 3
Since -1 divided by -8 is positive, -1 / (-2) ^ 3 equals 1/8.
Step 4: Simplify the expression 4 ^ 0 * 5 ^ -2 * (-2) ^ -3
Since any number raised to the power of 0 is always 1, the expression 4 ^ 0 becomes 1.
Also, 5 ^ -2 equals 1 / (5 ^ 2) = 1 / 25.
Finally, (-2) ^ -3 simplifies to 1/8 as determined in step 3.
Combining these values, the final simplified expression is 1 * (1/25) * (1/8) = 1/200.