Session 7: Surds and Exponents | A NEW OUTLOOK – CSIR-NET Series

jessepfrancisOctober 12, 2023October 16, 2023General AptitudeChristy Varghese, CSIR-NET, General Aptitude, JRF, YouTube Free Class

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Live Lecture

Exponent Form

When a number is multiplied by itself several times, it can be written in a short form with the help of exponents. Example: 5×5×5×5=5⁴. Here, 5⁴ is called an exponential expression.

The number multiplied by itself, again and again, is the base. The number of times the number appears or is multiplied is the exponent. In 5⁴, 5 is the base and 4 is the exponent.

Surds

The values in the square root or cube root or any other roots, which cannot be further simplified into whole numbers or integers, are known as a surd. Example: The value of √5.

Laws of Exponent

a^m× aⁿ = a^m+n
a^m/ aⁿ= a^m-n
a^m× b^m= (ab)^m
a^m/ b^m= (a/b)^m
(a^m)ⁿ = a^mn
${a^m}^n=a^{\left(m^n\right)}$
a^(1/m) = ^m√a
a^-m = 1/a^m
a^m/n = ⁿ√a^m
a⁰ = 1

Which of the following values is same as ${{2^2}^2}^2$ ? (CSIR-NET FEB 2022, JUNE 2017)

$2^6$

That’s wrong! Hint: $a^m^n=a^{\left(m^n\right)}$

$2^8$

That’s wrong! Hint: $a^m^n=a^{\left(m^n\right)}$

$2^{16}$

That’s right!

$2^{222}$

That’s wrong! Hint: $a^m^n=a^{\left(m^n\right)}$

$4^0+4^2+\frac{1}{4^2}+4^\frac{1}{2}+\frac{1}{4^\frac{1}{2}}$ equals (CSIR-NET December 2012)

$4^0$

That’s wrong! Hint: Use the laws of exponents!

$4^{2\frac{1}{2}}+4^{-2\frac{1}{2}}$

That’s wrong! Hint: Use the laws of exponents!

$19\frac{9}{16}$

That’s right!

$22\frac{9}{16}$

That’s wrong! Hint: Use the laws of exponents!

Some Important Expansions

(a + b)² = a² + 2ab + b²
(a – b)² = a² – 2ab + b²
a² – b²= (a + b)(a – b)
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a – b)³ = a³ – 3a²b + 3ab² – b³

Suppose $729^{22\over3} 81^{x\over2} = 3$ . The value of x is (CSIR-NET JUNE 2023)

-21

That’s wrong! Hint: 729 = 9 x 9 x 9, 81 = 9 x 9!

-21.5

That’s right!

-22

That’s wrong! Hint: 729 = 9 x 9 x 9, 81 = 9 x 9!

-20.5

That’s wrong! Hint: 729 = 9 x 9 x 9, 81 = 9 x 9!

Which of the following is the largest? (CSIR-NET JUNE 2019)

$2^{50}$

That’s wrong! Hint: Try making the exponent same!

$3^{40}$

That’s right!

$4^{30}$

That’s wrong! Hint: Try making the exponent same!

$5^{20}$

That’s wrong! Hint: Try making the exponent same!

Which of the following is the largest? (CSIR-NET JUNE 2017)

$2^{500}$

That’s wrong! Hint: Try making the base same!

$3^{400}$

That’s right!

$4^{300}$

That’s wrong! Hint: Try making the exponent same!

$5^{200}$

That’s wrong! Hint: Try making the exponent same!

Which of the following numbers is the largest? $2^{3^4}, 2^{4^3}, 3^{2^4}, 3^{4^2}, 4^{2^3}, 4^{3^2}$ (CSIR-NET DEC 2012)

$2^{3^4}$

That’s right!

$3^{4^2}$

That’s wrong! Hint: Try making the base same!

$4^{3^2}$

That’s wrong! Hint: Try making the base same!

$4^{2^3}$

That’s wrong! Hint: Try making the base same!

Here’s a comic to wind up the discussion:

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Christian. Artist. Mathematician. Programmer. Teacher. Visit https://mathematicos.in/aboutjesse/ for my full profile. View more posts

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