Question

Используя свойства степеней, найдите значение выражения: 1) а)2⁸×(2³)²:2¹²; б)7¹⁵:(7⁵)²:7³; 2) а)16²/2⁵; б)27⁴/9⁵; в)32³×8²/16⁵ 3) а)3¹⁰×7¹⁰/21⁸; б)6¹⁵/2¹³×3¹³; в)20¹⁰/5¹⁰×4¹⁰ Пожалуйста помогите срочно! Сразу ответ, решение не нужно. Дам 25 баллов

Answer 1

Ответ:

В решении.

Объяснение:

Используя свойства степеней, найдите значение выражения:

1)

а) 2⁸ * (2³)² : 2¹² =

= 2⁸ * 2⁶ : 2¹² =

= 2⁸⁺⁶⁻¹² = 2² = 4;  

б) 7¹⁵ : (7⁵)² : 7³ =

= 7¹⁵ : 7¹⁰ : 7³ =

= 7¹⁵⁻¹⁰⁻³ = 7² = 49;

2)

а) 16²/2⁵ = (2⁴)²/2⁵ = 2⁸/2⁵ = 2⁸⁻⁵ = 2³ = 8;

б) 27⁴/9⁵ = (3³)⁴/(3²)⁵ = 3¹²/3¹⁰ = 3¹²⁻¹⁰ = 3² = 9;

в) 32³ * 8² : 16⁵ = (2⁵)³ * (2³)² : (2⁴)⁵ = 2¹⁵ * 2⁶ : 2²⁰ = 2¹⁵⁺⁶⁻²⁰ = 2¹ = 2;

3)

а) 3¹⁰ * 7¹⁰ : 21⁸ = 3¹⁰ * 7¹⁰ : 3⁸ * 7⁸ = 3¹⁰⁻⁸ * 7¹⁰⁻⁸ = 3² * 7² = 21² = 441;

или:

а) 3¹⁰ * 7¹⁰ : 21⁸ = 21¹⁰ : 21⁸ = 21¹⁰⁻⁸ = 21² = 441;

б) 6¹⁵ : 2¹³ * 3¹³ = 2¹⁵ * 3¹⁵ : 2¹³ * 3¹³ = 2¹⁵⁻¹³ * 3¹⁵⁻¹³ = 2² * 3² = 6² = 36;

или:

6¹⁵ : 2¹³ * 3¹³ = 6¹⁵ : 6¹³ = 6² = 36;

в) 20¹⁰ : 5¹⁰ * 4¹⁰ = 20¹⁰ : 20¹⁰ = 1.

Answer 2

1) а) 2⁸×(2³)²:2¹²

To simplify this expression, we can use the properties of exponents. When multiplying two numbers with the same base, we add their exponents. When dividing two numbers with the same base, we subtract their exponents.

In this case, we have: 2⁸ × (2³)² ÷ 2¹²

Let's simplify each part separately: 2⁸ = 2^(8) = 256 (2³)² = (2^3)² = 8² = 64 2¹² = 2^(12) = 4096

Now, let's substitute these values back into the expression: 256 × 64 ÷ 4096

To simplify further, we can cancel out common factors: 256 ÷ 4096 = 1 ÷ 16 = 1/16

Therefore, the value of the expression is 1/16.

1) б) 7¹⁵:(7⁵)²:7³

Using the properties of exponents, we can simplify this expression: 7¹⁵ ÷ (7⁵)² ÷ 7³

Let's simplify each part separately: 7¹⁵ = 7^(15) (7⁵)² = (7^5)² = 16807² = 282475249

Now, let's substitute these values back into the expression: 7^(15) ÷ 282475249 ÷ 7³

To simplify further, we can cancel out common factors: 7^(15) ÷ 7³ = 7^(15-3) = 7¹²

Therefore, the value of the expression is 7¹².

2) а) 16²/2⁵

To simplify this expression, we can use the properties of exponents: 16² ÷ 2⁵

Let's simplify each part separately: 16² = 16^2 = 256 2⁵ = 2^5 = 32

Now, let's substitute these values back into the expression: 256 ÷ 32

To simplify further, we can cancel out common factors: 256 ÷ 32 = 8

Therefore, the value of the expression is 8.

2) б) 27⁴/9⁵

Using the properties of exponents, we can simplify this expression: 27⁴ ÷ 9⁵

Let's simplify each part separately: 27⁴ = 27^4 = 531441 9⁵ = 9^5 = 59049

Now, let's substitute these values back into the expression: 531441 ÷ 59049

To simplify further, we can cancel out common factors: 531441 ÷ 59049 = 9

Therefore, the value of the expression is 9.

2) в) 32³×8²/16⁵

To simplify this expression, we can use the properties of exponents: 32³ × 8² ÷ 16⁵

Let's simplify each part separately: 32³ = 32^3 = 32768 8² = 8^2 = 64 16⁵ = 16^5 = 1048576

Now, let's substitute these values back into the expression: 32768 × 64 ÷ 1048576

To simplify further, we can cancel out common factors: 32768 ÷ 1048576 = 1 ÷ 32 = 1/32

Therefore, the value of the expression is 1/32.

3) а) 3¹⁰×7¹⁰/21⁸

Using the properties of exponents, we can simplify this expression: 3¹⁰ × 7¹⁰ ÷ 21⁸

Let's simplify each part separately: 3¹⁰ = 3^10 = 59049 7¹⁰ = 7^10 = 282475249 21⁸ = 21^8 = 1801088541

Now, let's substitute these values back into the expression: 59049 × 282475249 ÷ 1801088541

To simplify further, we can cancel out common factors: 59049 ÷ 1801088541 = 1 ÷ 30581 = 1/30581

Therefore, the value of the expression is 1/30581.

3) б) 6¹⁵/2¹³×3¹³

To simplify this expression, we can use the properties of exponents: 6¹⁵ ÷ 2¹³ × 3¹³

Let's simplify each part separately: 6¹⁵ = 6^15 = 470184984576 2¹³ = 2^13 = 8192 3¹³ = 3^13 = 1594323

Now, let's substitute these values back into the expression: 470184984576 ÷ 8192 × 1594323

To simplify further, we can cancel out common factors: 470184984576 ÷ 8192 = 57468750

Therefore, the value of the expression is 57468750.

3) в) 20¹⁰/5¹⁰×4¹⁰

Using the properties of exponents, we can simplify this expression: 20¹⁰ ÷ 5¹⁰ × 4¹⁰

Let's simplify each part separately: 20¹⁰ = 20^10 = 10240000000000 5¹⁰ = 5^10 = 9765625 4¹⁰ = 4^10 = 1048576

Now, let's substitute these values back into the expression: 10240000000000 ÷ 9765625 × 1048576

To simplify further, we can cancel out common factors: 10240000000000 ÷ 9765625 = 1048576

Therefore, the value of the expression is 1048576.

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