ML Aggarwal: Exponents & Powers - 1

Q.1. Evaluate:

Let us evaluate the given expression,
By using the formula,
So,

(ii) (-3)^-3

^{Let us evaluate the given expression,} 
By using the formula,
So,

(iii) 

Let us evaluate the given expression,
By using the formula,
So,

Q.2. Simplify:

Let us simplify the given expression,

Let us simplify the given expression,

Let us simplify the given expression,

=
= 1

Let us simplify the given expression,


= 16

Q.3. Find the multiplicative inverse of the following:

Let us simplify to find the multiplicative inverse of the given expression,


So, the multiplicative inverse of 8/27 is 27/8.

Let us simplify to find the multiplicative inverse of the given expression,


So, the multiplicative inverse of 4/9 is 9/4.

Let us simplify to find the multiplicative inverse of the given expression,


So, the multiplicative inverse of 7/5 is 5/7.

Q.4. (i) Express 16^-2 as a power with base 2.
(ii) Express 125^-4 as a power with base 5.

(i) Express 16^-2 as a power with base 2.

Let us simplify,
(16)^-2 = (24)^-2
= 2^-8
=

(ii) Express 125-4 as a power with base 5. 

Let us simplify,
(125)^-4 = (53)^-4
= 5^-12
=

Q.5. Write the following numbers in expanded form using exponents:
(i) 2789.453
(ii) 3007.805

(i) 2789.453

The expanded form of
2789.453
= 2 × 10³ + 7 × 10² + 8 × 10¹ + 9 × 10⁰ + 4 × 10^-1 + 5 × 10^-2 + 3 × 10^-3 

(ii) 3007.805

The expanded form of
3007.805 = 3 × 10³ + 7 × 10⁰ + 8 × 10^-1 + 5 × 10^-3

Q.7. Simplify and write in exponential form with positive exponent:

Let us simplify,

The exponential form is .

Let us simplify,



The exponential form is .

Let us simplify,

=

The exponential form is .

Let us simplify,

= 2^-3+4 × 5³
= 2¹ × 5³
= 2 × 5 × 5 × 5
= 250
The exponential form is 250.

Q.7. Simplify and write the following in exponential form:

Let us simplify,

=
= 64 + 55^-3 - 1
= 64 + 52 - 1
= 64 + 25 - 1
= 88
The exponential form is 88.

Let us simplify,

= +
= 33 + (16×9) + 4/2 + 19
= 27 + 144 + 2 + 19
= 192
The exponential form is 192.

Q.8. Simplify and write in exponential form with negative exponent:

Let us simplify,

= 53^-3 × 4³
= 5⁰ × 4³
= 1 × 4³
=
The exponential form is .

Let us simplify,


The exponential form is .

Let us simplify,



The exponential form is .

Let us simplify,


=
The exponential form is .

Let us simplify,


The exponential form is .

Q.9. Simplify:

Let us simplify the given expression,

=
=

Let us simplify the given expression,


= 3^6+3-2-4 × t^4-2 
= 3³ × t²
= 27t

Let us simplify the given expression,

= 3^-4+10 × 5^-6+6 × t^-6+12
= 3⁶ × 5⁰ × t⁶
= 3⁶ × 1 × t⁶
= 729t⁶

Let us simplify the given expression,

= 2-5+2+5 × 3-5+5 × 5-5+3+6
= 2² × 3⁰ × 5⁴
= 4 × 1 × 625
= 2500

Q.10. By what number should be divided to get .

Let us simplify the expression,

Q.11. Find the value of m for which 9m ÷ 3-² = 9⁴. 

Let us simplify the expression,
9^m ÷ 3^-2 = 94(32)^m ÷ 3^-2
= (3²)⁴    3^2m ÷ 3^-2 = 38
32^m+2 = 38
Now by comparing the powers, we get
2m + 2 = 8       2m = 8 - 2             = 6
= 6/2m
m = 6/2 = 6

Q.12. If , find the value of x.

Let us simplify the given expression,


Now by comparing the powers, we get  
8 = 3x - 1
x = 8 + 9/3
= 3

Q.13. Let us simplify the given expression,

Now by comparing the powers,
we get -21 = -2x +1
2x = 1 + 21
2x = 22
x = 22.2
= 11

Q.14. (i) If , find x.

(ii)  , find n.

(i) If , find x.

Let us simplify the given expression,

Now by comparing the powers, we get
2x - 1 = -3x + 9
2x + 3x = 9 + 1
5x = 10
x = 10/5
x = 2

Let us simplify the given expression,

[3²ⁿ × 3⁵ × 3⁹] = (3×3¹⁶) = 3³
32^n+5+9-1-16 = 3³
Now by comparing the powers,
we get 2n + 5 + 9 - 1 - 16 = 3
2n - 3 = 3
2n = 3 + 3
2n = 6
n =6/2
= 3