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}