Question

answer answer answer with solution​

Answer 1

Answer:

Step-by-step explanation:

1. i) (3)⁻² = 1/(3)² = 1/9                           iv) (6)² = 36

ii) (-4)⁻²   = 1/(-4)² = 1/16                        v) (3)⁻³ = 1/(3)³ = 1/27

iii) (1/2)⁻⁵ = 1 / (1/2)⁵ = (2)⁵ = 64           vi) (1/3)⁻² =  1 / (1/3)² = 3² = 9

2. i)  (-4)⁵ / (-4)⁸ = (-4)⁵⁻⁸= (-4)⁻³ = 1/(-4)³ = 1/(-64)

ii)   (1/2³)² = 1/(2³ˣ²) = 1/(2⁶) = 1/64

iii) (-3)⁴ * (5/3)⁴ = 3⁴ * (5⁴ / 3⁴) = 5⁴ = 625

iv) ( 3⁻⁷ / 3⁻¹⁰) * 3⁻⁵  =( 3⁻⁷ ⁻ ⁽⁻¹⁰⁾ ) * 3⁻⁵ = (3⁻⁷⁺¹⁰) * 3⁻⁵

                              = 3³ * 3⁻⁵ = 3³⁺⁽⁻⁵⁾

                              = 3⁻² = 1/9

v) 2⁻³ * (-7)⁻³ = ( 1/2³) * (1/7³)

                    =( 1/8) * (1/343)

                    = 1/(8*343)

                    = 1/2744

vi) (-2)² * (-2)⁵ = (-2)²⁺⁵ = (-2)⁷ = -128

vii) (1/3²)³ = 1/(3⁶) = 729

viii) (-2)² * (2/3)³ = (-1 * 2)² * (2/3)³

                            = (-1)² * 2³ * (2³/3³)

                            = (2²⁺³)/3³

                            = 2⁵ / 3³

                           = 32/27

Answer 2

EXPONENTS and POWERS

Answer:

The solution to your question is attached along with this answer. Kindly have a look over it.

Important rules to follow while evaluating or simplifying exponents and powers are as follows:

1. $a^m * a^n = a^{m+n}$
2. $\frac{a^{m} }{a^{n}} = a^{m-n}$
3. $a^{m} * b^{m} = ab^{m}$
4. $\frac{a^{m}}{b^{m}} = (\frac{a}{b})^{m}$
5. $(a^{m})^{n} = a^{mn}$
6. $(a)^{-m} = \frac{1}{a^{m}}$
7. $\frac{1}{(a)^{-m}} = a^{m}$
8. $a^{0} = 1$