**Exponents worksheets2 :**

Here we are going to see some practice questions on exponents.

(1) Simplify (-7)² x (-3)³

(2) Simplify (-2)⁵ x (-1)⁸³

(3) Simplify (-4)⁵ ÷ (-4)⁸

(4) Simplify (-3)⁴ x (5/3)⁴

(5) Simplify (3⁻⁷÷ 3¹⁰) x 3⁻⁵

(6) Simplify

(7) Simplify

(8) Simplify

(9) Simplify

(10) Simplify

**Question 1 :**

Simplify (-7)² x (-3)³

**Solution :**

**Since the power of -7 is even, the answer must have positive sign. So we can just multiply 7 two times to find the value of **(-7)².

(-7)² = 7 x 7 ==> 49

**Since the power of -3 is odd, the answer will have negative sign.****So we can just multiply 3 three times to find the value of **(-3)³.

(-3)³ = (-3) x (-3) x (-3) ==> -27

(-7)² x (-3)³ = 49 x (-27) ==> -1323

Hence the answer is -1323

**Question 2 :**

Simplify (-2)⁵ x (-1)⁸³

**Solution :**

**Since we have odd power for -2 and -1, we will have negative sign for the expansions of **(-2)⁵ and (-1)⁸³.

Negative times negative is positive, so the final answer will have positive sign.

(-2)⁵ = 2 x 2 x 2 x 2 x 2 ==> -32

(-1)⁸³ = -1

(-2)⁵ x (-1)⁸³= 32

Hence the answer is 32.

**Question 3 :**

Simplify (-4)⁵ ÷ (-4)⁸

**Solution :**

**(-4)⁵ ÷ (-4)⁸ = **(-4)⁵ x (-4)⁻⁸

Since we change the division sign as multiplication. The exponent of the denominator is going to become negative.

= (-4)⁵⁻⁸ ==> (-4)⁻³

In order to make the power as positive, we are going to write the reciprocal of -4

= (-4)⁻³ ==> (-1/4)³

Since the power is odd the answer will have negative sign.

(-1/4)³ = -1/64

Hence the answer is -1/64.

**Question 4 :**

Simplify (-3)⁴ x (5/3)⁴

**Solution :**

(-3)⁴ x (5/3)⁴ = (3)⁴ x (5⁴/3⁴)

= 5⁴ ==> 5 x 5 x 5 x 5 ==> 625

**Question 5 :**

Simplify (3⁻⁷÷ 3¹⁰) x 3⁻⁵

**Solution :**

= (3⁻⁷÷ 3¹⁰) x 3⁻⁵

= (3⁻⁷x 3⁻¹⁰) x 3⁻⁵

= 3^(-7 -10 - 5) ==> 3^-22 ==> 1/3²²

**Question 6 :**

Simplify

**Solution :**

**Question 7 :**

Simplify

**Solution :**

**Question 8 :**

Simplify

**Solution :**

**Question 9 :**

Simplify

**Solution :**

= (-2)² + (-3)² + (-4)²

= 4 + 9 + 16 ==> 29

Hence the answer is 29.

**Question 10 :**

Simplify

**Solution :**

= (-3)⁴ ==> -81

Hence the answer is -81.

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