Find the value of 4 - 3 × t 5 × 45 t 3 × 4 - 5 × 15 2 .

We have, 4 - 3 × t 5 × 45 t 3 × 4 - 5 × 15 2 = 4 - 3 × t 5 × 15 × 3 t 3 × 4 - 5 × 15 2 = 4 - 3 × t 5 × 15 × 3 × t - 3 × 4 5 × 15 - 2 [Use a - m = 1 a m ] = 4 - 3 × t 5 × 15 × 3 × t - 3 × 4 5 × 15 - 2 = 4 - 3 + 5 × t 5 - 3 × 15 1 - 2 × 3 [Use a m × a n = a m + n ] = 4 2 × t 2 × 15 - 1 × 3 = 16 × t 2 × 3 15 = 16 t 2 5 Therefore, the required answer is 16 t 2 5 .

E M B I B E

Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 10 - Exponents and Powers>Exercise>Q 68

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IMPORTANT

Earn 100

Mohan divided a sum of rupees into two parts $5^{x}$ and $4^{x}$ and distributed it between his two sons, Parth and Ankur respectively. The product of $5^{x}$ and $4^{x}$ is $8000$

The amount of money received by Parth.

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Important Questions on Exponents and Powers

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IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 10 - Exponents and Powers>Exercise>Q 69

The exponent refers to the number of times a number is multiplied by itself. E.g. $\underset{n times}{\underset{⏟}{a \times a \times a \times . . . . . . \times a}} = a^{n}$ .

Find $1^{2^{3^{4^{5^{6^{7^{8}}}}}}}$ .

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IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 10 - Exponents and Powers>Exercise>Q 70

If

x = 2

and

y = 4

, then

{(\frac{x}{y})}^{x - y} + {(\frac{y}{x})}^{y - x} =

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IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 10 - Exponents and Powers>Exercise>Q 71

The size of a red blood cell is

0.000007 m

and that of a plant cell is

0.00001275 m

. What is the approximate ratio of their sizes?

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IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 10 - Exponents and Powers>Exercise>Q 72

If an average ant weighs

2 \times 10^{- 6} kg

and there are around

10

quintillion

= 10^{17}

ants in the world. If a human weighs

50 kg

and there are

8, 000, 000, 000

humans, then find the ratio of total weight of humans to the total weight of ants.

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Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 10 - Exponents and Powers>Exercise>Q 73

The usual form of

2.39461 \times 10^{6}

is _____.

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Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 10 - Exponents and Powers>Exercise>Q 74

Simplify

{[{(\frac{5}{2})}^{- 1} - {(\frac{1}{4})}^{- 1}]}^{- 1}

.

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IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 10 - Exponents and Powers>Exercise>Q 75

Simplify: ${[{(\frac{- 2}{3})}^{- 2}]}^{- 3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times \frac{1}{6}$ . If the answer is $\frac{3^{k}}{2^{p}}$ , find $k + p$ .