# Powers (exponents)

**Concept of
powers (exponents):**

A power
contains two parts exponent and base.

We know 2 × 2 × 2 × 2 = 2

^{4}, where 2 is called the base and 4 is called the power or exponent or index of 2.

**Reading Exponents**

**Examples on evaluating powers (exponents):**

**1. Evaluate each expression:**

**(i) **5

^{4}.

**Solution: **
5

^{4}
= 5 ∙ 5 ∙ 5 ∙ 5

→ Use 5 as a factor 4 times.

= 625

→ Multiply.

** (ii) ** (-3)

^{3}.

**Solution:**
(-3)

^{3}
= (-3) ∙ (-3) ∙ (-3)

→ Use -3 as a factor 3 times.

= -27

→ Multiply.

** (iii) **-7

^{2}.

**Solution: **
-7

^{2}
= -(7

^{2})

→ The power is only for 7 not for negative 7

= -(7 ∙ 7)

→ Use 7 as a factor 2 times.

= -(49)

→ Multiply.

= -49

** (iv) ** (2/5)

^{3}
**Solution: **
(2/5)

^{3}
= (2/5) ∙ (2/5) ∙ (2/5)

→ Use 2/5 as a factor 3 times.

= 8/125

→ Multiply the fractions

**Writing Powers (exponents) **

**2.
Write each number as the power of a given base:**

** (a) **16; base 2

**Solution: **
16; base 2

Express 16 as an exponential form where base is 2

The product of four 2’s is 16.

Therefore, 16

= 2 ∙ 2 ∙ 2 ∙ 2

= 2

^{4}
Therefore, required form = 2

^{4}
** (b) ** 81; base -3

**Solution: **
81; base -3

Express 81 as an exponential form where base is -3

The product of four (-3)’s is 81.

Therefore, 81

= (-3) ∙ (-3) ∙ (-3) ∙ (-3)

= (-3)

^{4}
Therefore, required form = (-3)

^{4}
** (c) **-343; base -7

**Solution: **
-343; base -7

Express -343 as an exponential form where base is -7

The product of three (-7)’s is -343.

Therefore, -343

= (-7) ∙ (-7) ∙ (-7)

= (-7)

^{3}
Therefore, required form = (-7)

^{3}
`

**Algebra 1**

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