LAWS OF EXPONENTS WORKSHEET

Detailed Solution

Problem 1 :

5⁴ x 5⁷

Solution :

= 5⁴ x 5⁷

Since the bases are same, we have to use only one base and add the powers.

= 5⁴⁺⁷

= 5¹¹

Problem 2 :

d² x d⁶

Solution :

= d² x d⁶

Since the bases are same, we have to use only one base and add the powers.

= d^{2 + 6}

= d⁸

Problem 3 :

k⁸ ÷ k³

Solution :

= k⁸ ÷ k³

Since the bases are same, we have to use only one base and subtract the powers.

= k^{8 - 3}

= k⁵

Problem 4 :

7⁵ ÷ 7⁶

Solution :

= 7⁵ ÷ 7⁶

Since the bases are same, we have to use only one base and subtract the powers.

= 7^{5 - 6}

= 7^-1

By changing the negative exponent as positive, we have to change flip the base.

= (1/7)¹

= 1/7

So, the answer is 1/7.

Problem 5 :

(x²)⁵

Solution :

= (x²)⁵

Since we have power raised by another power, we have to multiply the powers.

= x^2·5

= x¹⁰

So, the answer is x¹⁰.

Problem 6 :

(3⁴)⁴

Solution :

= (3⁴)⁴

Since we have power raised by another power, we have to multiply the powers.

= 3^4·4

= 3¹⁶

So, the answer is 3¹⁶.

Problem 7 :

p³ ÷ p⁷

Solution :

= p³ ÷ p⁷

Since the bases are same, we have to use only one base and subtract the powers.

= p^{3 - 7}

= p^-4

By changing the negative exponent as positive, we have to change flip the base.

= (1/p)⁴

= 1/p⁴

So, the answer is 1/p⁴.

Problem 8 :

n⁹ x n³

Solution :

= n⁹ x n³

Since the bases are same, we have to use only one base and add the powers.

= n^{3 + 9}

= n¹²

Problem 9 :

(5^t)³

Solution :

= (5^t)³

Since we have power raised by another power, we have to multiply the powers.

= 5^t(3)

= 5^3t

Problem 10 :

7^x · 7²

Solution :

= 7^x · 7²

Since bases are multiplied, we have to put the base once and add the powers. 

= 7^{(x + 2)}

So, the answer is 7^{(x + 2)}.

Problem 11 :

10³ ÷ 10^q

Solution :

= 10³ ÷ 10^q

Since bases are divided, we have to put only one base and subtract the powers.

= 10^{3 - q}

Problem 12 :

(c⁴)^m

Solution :

= (c⁴)^m

Since we have power raised by another power, we have to multiply the powers.

= c^4m

Problem 13 :

(6x²) (4x²)

Solution :

= (6x²) (4x²)

First we have to multiply signs, then multiply the coefficients. Finally multiply the variables.

= 6 (4) x²x²

= 24 x^{2 + 2}

= 24 x⁴

Problem 14 :

(3x³y²)(-6 y⁵)

Solution :

= (3x³y²)(-6 y⁵)

First we have to multiply signs, then multiply the coefficients. Finally multiply the variables.

= 3 (6) x³ y² y⁵

= 24 x^{2 + 2}

= 24 x⁴

= 24 x⁴

Problem 15 :

 (5p³)(-m⁸ p²)

Solution :

=  (5p³)(-m⁸ p²)

First we have to multiply signs, then multiply the coefficients. Finally multiply the variables.

= 5(-1) p³p²m⁸

= -5 p²⁺³m⁸

= -5 p⁵m⁸

Problem 16 :

 (10g³ h⁸ v⁶) (11g h⁸)

Solution :

=   (10g³ h⁸ v⁶) (11g h⁸)

First we have to multiply signs, then multiply the coefficients. Finally multiply the variables.

= 10 (11) g³ · g h⁸· h⁸ v⁶

= 110 g^{(3 + 1)} h⁽⁸⁺⁸⁾v⁶

= 110 g⁴ h¹⁶v⁶

Problem 17 :

(4 f⁹ h³) (-5 f⁶) (-3 h²) 

Solution :

= (4 f⁹ h³) (-5 f⁶) (-3 h²) 

First we have to multiply signs, then multiply the coefficients. Finally multiply the variables.

= 4(-5)(-3) f⁹ · f⁶ h³ · h²

= -60 f⁹⁺⁶ h³⁺²

= -60 f¹⁵ h⁵

Problem 18 :

(-2² x³ y⁴)((-3)² x⁴ y⁴)

Solution :

= (-2² x³ y⁴)((-3)² x⁴ y⁴)

First we have to multiply signs, then multiply the coefficients. Finally multiply the variables.

= 4(-3)²x³ · x⁴ y³ · y⁴ 

= 36 x³⁺⁴ y³⁺⁴

= 36 x⁷ y⁷

Problem 19 :

(3 x^a y^b z^c )(-y^f z^g )

Solution :

=  (3 x^a y^b z^c )(-y^f z^g )

First we have to multiply signs, then multiply the coefficients. Finally multiply the variables.

= 3(-1) x^a  y^b z^cz^g

= -3 x^a  y^b z^c+g

Problem 20 :

(x² y)⁴

Solution :

= (x² y)⁴

Here we have to distribute the power for all the terms which are inside the bracket.

= (x²)⁴ y⁴

Since we have power raised by another power, we have to multiply the powers.

= x²⁽⁴⁾ y⁴

= x⁸ y⁴

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