# Exponents And Power

Exercise 1

1. Evaluate.

(i) 3–2 (ii) (– 4)– 2  Answer: = 2²+3²+4² = 4+9+16 = 29

2. Simplify and express the result in power notation with positive exponent.    Alternate Method:

= -34 x 54 ÷34 (the power on 3 is even so -34 = 34)

=30 x 54=625

(iv) (3–7 ÷Answer: Using am÷ an = am-n

(3–7 ÷ 3–10) = 3-7+10 = 33

Hence, (3–7 ÷ 3–10) �— 3–5

=33 x 3–5

Now, am x an = am+n

Hence, = 33 x 3–5

= 33-5 = 3-2

(v) 2– 3 �— (–7)–3 3. Find the value of.

(i) (3° + 4–1) �— 22

Answer: (3° + 4–1) �— 22 (ii) (2–1 �— 4–1) ÷ 2–2 (iii) (3–1 + 4–1 + 5–1)0

Hence, (3–1 + 4–1 + 5–1)0 = 1 4. Evaluate (ii) (5–1 �— 2–1) �— 6–1 5. Find the value of m for which 5m ÷ 5–3 = 55

Here, m-n = 5 and n = -3

So, m = 5+(-3)=2

6. Evaluate  7. Simplify.

(i) (25 x t-4) ÷ (5-3 x 10 x t-8)

Answer: (25 x t-4) ÷ (5-3 x 10 x t-8)

=(5² x t-4) ÷ (5-3 x 5 x 2 x t-8)

= 52+2 x t-4+8 ÷ 2

= 54 x t4 ÷ 2

(ii) (3-5 x 10-5 x 125) ÷ (5-7 x 6-5)

= (3-5 x 5-5 x 2-5 x 53) ÷ (5-7 x 6-5)

= (3-5 x 5-5+3 x 2-5) ÷ (5-7 x 6-5)

= (3-5 x 5-2 x 2-5) ÷ (5-7 x 3-5 x 2-5)

= (3-5+5 x 5-2+7 x 2-5+5)

= (30 x 55 x 20)

=3125

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