(15 ^ 0 * 7 ^ - 2)/((- 4) ^ - 3)
(15 ^ 0 * 7 ^ - 2)/((- 4) ^ - 3) is equal to:
(1 * 1/49)/(-1/64)
Now, let's simplify this expression:
1 * 1/49 = 1/49
Therefore, our expression becomes:
(1/49)/(-1/64)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(1/49) * (-64/1) = -64/49
Therefore, (15 ^ 0 * 7 ^ - 2)/((- 4) ^ - 3) is equal to -64/49.
To solve the expression (15 ^ 0 * 7 ^ -2) / ((-4) ^ -3) step-by-step, follow these steps:
Step 1: Evaluate the exponents:
15 ^ 0 = 1 (any number raised to the power of 0 equals 1)
7 ^ -2 = 1/7^2 = 1/49 (negative exponent means taking the reciprocal of the base number)
(-4) ^ -3 = 1/(-4)^3 = 1/(-64) = -1/64 (negative exponent means taking the reciprocal of the base number)
Step 2: Substitute the evaluated exponents back into the expression:
(1 * (1/49)) / (-1/64)
Step 3: Simplify the expression:
Multiply fractions by multiplying the numerators together and the denominators together:
1 * 1/49 = 1/49
(-1/64) = -1/64
So, the expression simplifies to:
(1/49) / (-1/64)
Step 4: To divide by a fraction, multiply by its reciprocal:
(1/49) * (-64/1) = -64/49
Therefore, the expression (15 ^ 0 * 7 ^ -2) / ((-4) ^ -3) simplifies to -64/49.