EXPONENTS AND SQUARE ROOTS WORKSHEETS

About "Exponents and square roots worksheets"

Exponents and square roots worksheets :

Here we are going to see some practice questions based on the topic exponents and square root.

(1) Simplify the following

(-4)⁵ ÷ (-4)

(2) Simplify the following

3⁴ x 3³

(3) Simplify the following

(3/8)⁵ x (3/8)⁴ ÷ (3/8)

(4) Simplify the following

(2²)³/(3²)²

(5) Find the value of x

(2/8)^(2x) (2/8)^x = (2/8)^6

(6) Find the square root of the following

5 x 5 x 11 x 11 x 7 x 7

(7) Find the square root of the following

√(25a²) x √(49a)

(8) Find the square root of the following

∛125g³

(9) Find the square root of the following

√(9/64)

(10) Find the square root of the following

√2.56

Exponents and square roots worksheets - Solution

Problem 1 :

Simplify the following

(-4)⁵ ÷ (-4)

Solution :

(-4)⁵ ÷ (-4)⁸ = (-4)⁵ / (-4)

Since both terms are having same base, we have to put only one base and subtract the powers.

= (-4)⁸ ==> (-4) ³

=  1/(-4)³ ==> -1/64

Problem  2 :

Simplify the following

3x 3³

Solution :

3⁴ x 3³

If we want to multiply two or more terms which are multiplying with the same base, then we have to put only one base and add the powers.

= 3³ ==>  3

Problem 3 :

Simplify the following

(3/8)⁵ x (3/8)⁴ ÷ (3/8)

Solution :

=  (3/8)^(5 + 4 - 9)

=  (3/8)^(9 - 9)

=  (3/8)^⁰ ==> 1

Problem 4 :

Simplify the following

(2²)³/(3²)²

Solution :

=  (2²)³/(3²)²

=  2/3⁴ ==> 32/81

Problem 5 :

Find the value of x

(2/8)^(2x) (2/8)^x = (2/8)^6

Solution :

(2/8)^(2x) (2/8)^x = (2/8)^6

Put only one base and add the powers,

(2/8)^(2x+x) = (2/8)^6

(2/8)^(3x) = (2/8)^6

Since we have same bases on both sides, the powers are also equal.

3x = 6

Dividing by 3 on both sides, we get x = 2

=  2/3⁴ ==> 32/81

Problem 6 :

Find the square root of the following

5 x 5 x 11 x 11 x 7 x 7

Solution :

=  √(5 x 5 x 11 x 11 x 7 x 7)

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

So we can take one 5, one 11 and one 7.

=  5 x 11 x 7 ==> 385

Problem 7 :

Find the square root of the following

√(25a²) x √(49a)

Solution :

=  √(25a²) x √(49a)

=  √(5 x 5 x a x a  x 7 x 7 x a)

=  5 x a x 7 √a ==> 245 a

Problem 8 :

Find the square root of the following

∛125g³

Solution :

=  ∛125g³

=  (5 x 5 x 5 x g  x g x g)

Inside the cube root, if the same number is repeated three times, take one number out of the radical sign.

=  5 g

Problem 9 :

Find the square root of the following

√(9/64)

Solution :

Take square root for both numerator and denominator separately,

=  √9/64

=  √(3x3)/√(8x8)

=  3/8

Problem 10 :

Find the square root of the following

√2.56

Solution :

In order to remove the decimal point we have to multiply and divide by 100.

=  √2.56 x (100/100)

=  √(256/100)

√(16 x 16)/(10x10) ==> 16/10 ==> 1.6

=  √(3x3)/√(8x8)

=  3/8

After having gone through the stuff given above, we hope that the students would have understood "Exponents and square roots worksheets".

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