Question

7^-8 * 7^-9 : (7^3)^-5

Answer 1

7⁻⁸ * 7⁻⁹ : (7³)⁻⁵ = -8+(-9)-3*(-5) = -17 - (-15) = 7⁻²

Ответ: 7⁻²

Answer 2

To simplify the expression, you can use the properties of exponents. The general rule for simplifying expressions with the same base is to add or subtract the exponents:

1. When you multiply two numbers with the same base, you add the exponents: a^m * a^n = a^(m + n)
2. When you divide two numbers with the same base, you subtract the exponents: a^m / a^n = a^(m - n)
3. When you raise a power to another power, you multiply the exponents: (a^m)^n = a^(m * n)

Using these rules, let's simplify the expression step-by-step:

1. Simplify the numerator (7^-8 * 7^-9): 7^-8 * 7^-9 = 7^(-8 - 9) = 7^-17

2. Simplify the denominator ((7^3)^-5): (7^3)^-5 = 7^(3 * -5) = 7^-15

Now the entire expression becomes:

7^-17 / 7^-15

3. Apply the division rule (subtract the exponents): 7^-17 / 7^-15 = 7^(-17 - (-15)) = 7^-2

Therefore, the simplified expression is 7^-2, which can also be written as 1/7^2 or 1/49.