Chapter 8: Exponents and Powers

Ans: positive.

Ans: ${\left( {10} \right)^{ - 5}}$

As, xm × xn = (x)m+n

${10^5} \times {10^{ - 10}} = {\left( {10} \right)^{5 - 10}} = {\left( {10} \right)^{ - 5}}$

Ans: ${\left( {\dfrac{2}{{13}}} \right)^{ - 36}}$

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

Thus, 

${\left( {{{\left( {\dfrac{2}{{13}}} \right)}^{ - 6}} \div {{\left( {\dfrac{2}{{13}}} \right)}^3}} \right)^3} \times {\left( {\dfrac{2}{{13}}} \right)^{ - 9}} = {\left( {{{\left( {\dfrac{2}{{13}}} \right)}^{ - 6 - 3}}} \right)^3} \times {\left( {\dfrac{2}{{13}}} \right)^{ - 9}}$

= ${\left( {{{\left( {\dfrac{2}{{13}}} \right)}^{ - 9}}} \right)^3} \times {\left( {\dfrac{2}{{13}}} \right)^{ - 9}}$

= ${\left( {\dfrac{2}{{13}}} \right)^{ - 27}} \times {\left( {\dfrac{2}{{13}}} \right)^{ - 9}} = {\left( {\dfrac{2}{{13}}} \right)^{ - 27 - 9}} = {\left( {\dfrac{2}{{13}}} \right)^{ - 36}}$

Ans: $\dfrac{{18}}{{11}}$

Use the law of exponent ${a^{ - m}} = \dfrac{1}{{{a^m}}}$, where a is a non zero integer.

Thus, 

${\left( {{4^{ - 1}} + {3^{ - 1}} + {6^{ - 2}}} \right)^{ - 1}} = {\left( {\dfrac{1}{4} + \dfrac{1}{3} + \dfrac{1}{{{6^2}}}} \right)^{ - 1}}$

= ${\left( {\dfrac{1}{4} + \dfrac{1}{3} + \dfrac{1}{{36}}} \right)^{ - 1}} = {\left( {\dfrac{{9 + 12 + 1}}{{36}}} \right)^{ - 1}}$

= ${\left( {\dfrac{{22}}{{36}}} \right)^{ - 1}} = \dfrac{{36}}{{22}} = \dfrac{{18}}{{11}}$

Ans: 1

Use the law of exponent ${a^0} = 1$, where a is a non zero integer.

Thus, 

${\left( {{2^{ - 1}} + {3^{ - 1}} + {4^{ - 1}}} \right)^0} = 1$

Ans:  1 × 10-8

Standard form, $\dfrac{1}{{100000000}} = \dfrac{1}{{1 \times {{10}^8}}} = {10^{ - 8}}$

Ans: 1.234 x 107

For standard form of 12340000= 1234 x 104

= 1.234 x 104 x 103 = 1.234 x 107

Ans: 3410000

So, 3.41 x 106 = 3.41 x 10 x 10 x 10 x 10 x 10 x 10

= 3.41 x 106 = 3410000

Ans: 2394610

So, 2.39461 × 106 = 2.39461x 10 x 10 x 10 x 10 x 10 x 10

= 2.39461 x 106 = 2394610

Ans: ${6^{ - 2}}$

Since 36 = 6 × 6 = 62

Then $\dfrac{1}{{36}} = \dfrac{1}{{6 \times 6}} = \dfrac{1}{{{6^2}}} = {6^{ - 2}}$