cbse.media

Exercise Set 1

1. Express the number 32400 as a product of its prime factors in exponential form.

Solution: We perform prime factorization of 32400.

\begin{aligned} 32400 &= 324 \times 100 \\ &= 18^2 \times 10^2 \\ &= (2 \times 3^2)^2 \times (2 \times 5)^2 \\ &= (2^2 \times 3^4) \times (2^2 \times 5^2) \\ &= 2^{2+2} \times 3^4 \times 5^2 \\ &= 2^4 \times 3^4 \times 5^2 \end{aligned}

2. What is $(-1)^5$ ? Is it positive or negative? What about $(-1)^{56}$ ?

Solution:

$(-1)^5 = (-1) \times (-1) \times (-1) \times (-1) \times (-1) = -1$ . Since the exponent (5) is odd, the result is negative.
$(-1)^{56}$ . The exponent (56) is even. Therefore, the result is positive ( $+1$ ).

3. Is $(-2)^4 = 16$ ? Verify.

Solution: $(-2)^4 = (-2) \times (-2) \times (-2) \times (-2)$ $= 4 \times 4 = 16$ Yes, it is correct.

4. Express the following in exponential form:

(i) $6 \times 6 \times 6 \times 6 = 6^4$
(ii) $y \times y = y^2$
(iii) $b \times b \times b \times b = b^4$
(iv) $5 \times 5 \times 7 \times 7 \times 7 = 5^2 \times 7^3$
(v) $2 \times 2 \times a \times a = 2^2 \times a^2 = (2a)^2$
(vi) $a \times a \times a \times c \times c \times c \times c \times d = a^3 c^4 d$