Chapter 8: Exponents and Powers

Ans: ${3^4}$

Let a to be multiplied.

${\left( {\dfrac{5}{3}} \right)^4} \times a = {5^4}$

$\Rightarrow \dfrac{{{5^4}}}{{{3^4}}} \times a = {5^4}$

$\Rightarrow a = {3^4}$

Ans: ${3^{11}}$

Use the law of exponent ${a^m} \div {a^n} = {\left( a \right)^{m - n}}$, where a is a non zero integer.

Thus, 

${3^5} \div {3^{ - 6}} = {3^{5 - \left( { - 6} \right)}} = {3^{5 + 6}} = {3^{11}}$

Ans: 0.0000003

Given, 3 x 10-7   = 3.0 x 10-7   
Now, placing the decimal seven places towards the left of the original position, we get 0.0000003. Hence, the value of 3 x 10-7 is equal to 0.0000003.

Ans: equal

To add the numbers given in standard form, we first convert them into numbers with equal exponents.
e.g. 2.46 x 106   + 24.6 x 105 = 2.46 x 105 + 2.46 x 106 = 4.92 x 106

Ans: For standard form, 32500000000 = 3250 x 102 x 102 x 103

= 3250 x 107 = 3.250 x 1010 or 3.25 x 1010

Hence, the standard form for 32500000000 is 3.25 x 1010.

Ans: 8.0 x 10-9

For standard form, 0.000000008 = 0.8 x 10-8 = 8 x 10-9 = 8.0 x 10-9

Hence, the standard form for 0.000000008 is 8.0 x 10-9.

Ans: 0.00000000023

For usual form, 2.3 x 10-10 = 0.23 x 10-11
= 0.00000000023
Hence, the usual form for 2.3 x 10-10 is 0.00000000023.

Ans: 84

Since $\dfrac{{{8^5}}}{{{8^4}}} = 8$.

Ans: 210

As ${2^{10}} \times {2^{ - 5}} = {2^{10 - 5}} = {2^5}$

Ans: $\dfrac{1}{{{3^2} \times {4^2}}}$

As, ${\left( {{3^{ - 1}} \times {4^{ - 1}}} \right)^2} = {\left( {\dfrac{1}{3} \times\dfrac{1}{4}} \right)^2} = \dfrac{1}{{{3^2} \times {4^2}}}$