Express the following in exponential form:
(i) 5 × 5 × 5 × 5 × 5
(ii) 4 × 4 × 4 × 5 × 5 × 5
(iii) (-1) × (-1) × (-1) × (-1) × (-1)
(iv) a × a × a × b × c × c × c × d × d

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Solution

(i) 5 × 5 × 5 × 5 × 5 = (5)⁵
(ii) 4 × 4 × 4 × 5 × 5 × 5 = 4³ × 5³
(iii) (-1) × (-1) × (-1) × (-1) × (-1) = (-1)⁵
(iv) a × a × a × b × c × c × c × d × d = a³b¹c³d²

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Q. Simplify and express following in exponential form :

\frac{4^{5} \times a^{3} b^{3}}{4^{5} \times a^{5} b^{2}}

Q. Express the following in exponential form:
(i)

6 \times 6 \times 6 \times 6

(ii)

t \times t

(iii)

b \times b \times b \times b

(iv)

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(v)

2 \times 2 \times a \times a

(vi)

a \times a \times a \times c \times c \times c \times c \times d

A particle experiences a constant acceleration for 20 sec after starting from rest. If it travels a distance $S_{1}$ in the first 10 sec and a distance $S_{2}$ in the next 10 sec, then

S_{1}

and

S_{2}

are two spheres of equal masses.

S_{1}

runs down a smooth inclined plane of length 5 cm and of height 4 cm.

S_{2}

falls vertically down by 4 cm. the work done by all forces acting on

S_{1}

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Express the following in exponential form: (i) 5 × 5 × 5 × 5 × 5 (ii) 4 × 4 × 4 × 5 × 5 × 5 (iii) (-1) × (-1) × (-1) × (-1) × (-1) (iv) a × a × a × b × c × c × c × d × d

(i) 5 × 5 × 5 × 5 × 5 = (5)5 (ii) 4 × 4 × 4 × 5 × 5 × 5 = 43 × 53 (iii) (-1) × (-1) × (-1) × (-1) × (-1) = (-1)5 (iv) a × a × a × b × c × c × c × d × d = a3b1c3d2

Express the following in exponential form:
(i) 5 × 5 × 5 × 5 × 5
(ii) 4 × 4 × 4 × 5 × 5 × 5
(iii) (-1) × (-1) × (-1) × (-1) × (-1)
(iv) a × a × a × b × c × c × c × d × d

(i) 5 × 5 × 5 × 5 × 5 = (5)⁵
(ii) 4 × 4 × 4 × 5 × 5 × 5 = 4³ × 5³
(iii) (-1) × (-1) × (-1) × (-1) × (-1) = (-1)⁵
(iv) a × a × a × b × c × c × c × d × d = a³b¹c³d²