ГДЗ до підручника «Алгебра» О.С. Істера. 7 клас

122. 1) 3⁵ • 3² = 3^5+x; x = 2;

2) 2⁷ • 2⁸ = 2^1+x; x = 14;

3) 4^x • 4⁵ = 4⁸; x = 3;

4) 9⁸ : 9^x = 9⁵; x = 3.

123. 1) a² • a⁵ = a⁷;

2) a⁸ • a¹ = a⁹;

3) a⁴ • a⁸ • a⁷ = a¹⁹.

124. 1) b⁷ : b⁴ = b³;

2) b¹⁴ : b⁵ = b⁹;

3) b⁹ : b⁵ • b³ = b⁷;

4) b¹⁵ : b^{9 •} b⁴ = b¹⁰.

125. 1) 1,8⁹ : 1,8 = 1,8^9-x;

9 - 1 = 9 - x; x = 1;

2) 19^x : 19⁷ = 19⁹; x = 16;

3) 4¹² : 4^x = 4⁷; x = 5.

126. 1) 8⁷ = (2³)⁷ = 2²¹;

(16²)⁵ = ((2⁴)²)⁵ = 2⁴⁰;

2) 25³ = (5²)³ = 5⁶;

625⁷ = (5⁴)⁷ = 5²⁸.

127. 1) 9⁷ = (3²)⁷ = 3¹⁴;

(81²)⁵ = ((3⁴)^x)⁵ = 3⁴⁰;

2) 100⁴ = (10²)⁴ = 10⁸;

1000⁹ = (10³)⁹ = 10²⁷.

129. 1) x⁵ • xⁿ = x⁵⁺ⁿ;

2) x⁸ : xⁿ = x^8-n;

3) xⁿ : (x⁸ • x⁹) = xⁿ : x¹⁷ = x^n-17;

4) x²ⁿ : xⁿ • x³ⁿ⁺¹ = x⁴ⁿ⁺¹;

5) ((xⁿ)³)⁵ = x¹⁵ⁿ;

6) (-x⁴)²ⁿ = x⁸ⁿ.