Question

Найдите значение выражения:а)(64*4^-5)²б)5^-3*5^-1_______5^-6в)(128*2^-6)г)3^-9_______3^-2*3^-6вот эта черточка это дробная черта _____СРОЧНО ПОЖАЛУЙСТА!!!УМОЛЯЮ!!!

Answer 1

Не уверена что правильно)

Answer 2

a) (64 * 4^-5)²

To find the value of the expression (64 * 4^-5)², we can simplify it step by step.

First, let's simplify the expression inside the parentheses: 64 * 4^-5.

The exponent -5 means that we need to take the reciprocal of the base raised to the power of 5. So, 4^-5 is equal to 1 / 4^5.

Next, let's calculate 4^5. This is equal to 4 * 4 * 4 * 4 * 4, which is 1024.

Therefore, 4^-5 is equal to 1 / 1024.

Now, let's substitute this value back into the original expression: 64 * (1 / 1024).

Multiplying 64 by 1 / 1024 gives us 64 / 1024, which simplifies to 1 / 16.

Finally, let's square this result: (1 / 16)².

Squaring a fraction means multiplying the numerator and denominator by itself. So, (1 / 16)² is equal to (1 * 1) / (16 * 16), which simplifies to 1 / 256.

Therefore, the value of the expression (64 * 4^-5)² is 1 / 256.

б) 5^-3 * 5^-1 / 5^-6

To find the value of the expression 5^-3 * 5^-1 / 5^-6, we can simplify it step by step.

First, let's simplify the exponents: 5^-3, 5^-1, and 5^-6.

The exponent -3 means that we need to take the reciprocal of the base raised to the power of 3. So, 5^-3 is equal to 1 / 5^3.

Similarly, 5^-1 is equal to 1 / 5^1, and 5^-6 is equal to 1 / 5^6.

Next, let's calculate 5^3, 5^1, and 5^6. These are equal to 125, 5, and 15625, respectively.

Therefore, 5^-3 is equal to 1 / 125, 5^-1 is equal to 1 / 5, and 5^-6 is equal to 1 / 15625.

Now, let's substitute these values back into the original expression: (1 / 125) * (1 / 5) / (1 / 15625).

Dividing by a fraction is the same as multiplying by its reciprocal. So, (1 / 125) * (1 / 5) / (1 / 15625) is equal to (1 / 125) * (1 / 5) * (15625 / 1).

Multiplying the numerators and denominators gives us (1 * 1 * 15625) / (125 * 5 * 1), which simplifies to 15625 / 625.

Finally, let's simplify this fraction: 15625 / 625 is equal to 25.

Therefore, the value of the expression 5^-3 * 5^-1 / 5^-6 is 25.

в) (128 * 2^-6)

To find the value of the expression (128 * 2^-6), we can simplify it step by step.

The exponent -6 means that we need to take the reciprocal of the base raised to the power of 6. So, 2^-6 is equal to 1 / 2^6.

Next, let's calculate 2^6. This is equal to 2 * 2 * 2 * 2 * 2 * 2, which is 64.

Therefore, 2^-6 is equal to 1 / 64.

Now, let's substitute this value back into the original expression: 128 * (1 / 64).

Multiplying 128 by 1 / 64 gives us 128 / 64, which simplifies to 2.

Therefore, the value of the expression (128 * 2^-6) is 2.

г) 3^-9 / (3^-2 * 3^-6)

To find the value of the expression 3^-9 / (3^-2 * 3^-6), we can simplify it step by step.

First, let's simplify the exponents: 3^-9, 3^-2, and 3^-6.

The exponent -9 means that we need to take the reciprocal of the base raised to the power of 9. So, 3^-9 is equal to 1 / 3^9.

Similarly, 3^-2 is equal to 1 / 3^2, and 3^-6 is equal to 1 / 3^6.

Next, let's calculate 3^9, 3^2, and 3^6. These are equal to 19683, 9, and 729, respectively.

Therefore, 3^-9 is equal to 1 / 19683, 3^-2 is equal to 1 / 9, and 3^-6 is equal to 1 / 729.

Now, let's substitute these values back into the original expression: (1 / 19683) / (1 / 9 * 1 / 729).

Dividing by a fraction is the same as multiplying by its reciprocal. So, (1 / 19683) / (1 / 9 * 1 / 729) is equal to (1 / 19683) * (9 / 1) * (729 / 1).

Multiplying the numerators and denominators gives us (1 * 9 * 729) / (19683 * 1 * 1), which simplifies to 6561 / 19683.

Finally, let's simplify this fraction: 6561 / 19683 is equal to 1 / 3.

Therefore, the value of the expression 3^-9 / (3^-2 * 3^-6) is 1 / 3.

The fraction line (the horizontal line used to separate the numerator and denominator in a fraction) is represented by a forward slash (/) in the expression.

I hope this helps! Let me know if you have any further questions.