Question

Find the value of the following. (i)(-4)² (ii) (–3)×(–2)³ (iii)(-2)³×(-10)³​

Answer 1

Answer:

Step-by-step explanation:

Given that,

1) (-4)² = (-4) × (-4) = 16 ( ∵ - × - = + )

2) (-3) × (-2)³= (-3) × (-2) × (-2) × (-2) = (6) × (4) ( ∵ - × - = + )

= 24

3) (-2)³ = (-2) × (-2) × (-2) = (4) × (-2) ( ∵ - × - = + )

= -8 ( ∵ - × + = - )

4) (-2)³ × (-10)³ = (-2) × (-2) × (-2) × (-10) × (-10) × (-10)

= (4) × (-2) × (-10) × (-10) × (-10) (∵ - × - = +)

= (-8) × (-10) × (-10) × (-10) ( ∵ + × - = -)

= (80) × (-10) × (-10) ( ∵ - × - = + )

= (-800) × (-10) ( ∵ + × - = - )

= 8000 ( ∵ - × - = + )

Answer 2

Given that:-

$(i)(-4)^2\\(ii) (-3)\times (-2)^3\\(iii) (-2)^3\times (-10)^3$

As we have to find out the value of the given exponent.

Power or exponent is nothing but the higher-order power of some other number but the power can also be negative.

$(i) (-4)^2$

As the number 4 has the power of 2 which means we have to multiply the number twice,

$=>(-4)\times (-4)$

When we multiply the two negative terms we get positive, so we get

$=>16$

Hence, the value of $(-4)^2$ is $16.$

$(ii) (-3)\times (-2)^3$

As the number 2 has the power of 3 which means we have to multiply the number three times,

$=>(-3)\times[ (-2)\times (-2) \times (-2)]$

$=>(-3)\times (-8)$

When we multiply the two negative terms we get positive, so we get

$=>24$

Hence, the value of $(-3)\times (-2)^3$ is $24.$

$(iii) (-2)^3\times (-10)^3$

As the number 2 has the power of 3 which means we have to multiply the number two times and the number 10 has the power of 3 which means we have to multiply the number three times,

$=>[(-2)\times(-2)\times (-2)]\times[(-10)\times(-10)\times(-10)]$

$=>(-8)\times(-1000)$

When we multiply the two negative terms we get positive, so we get

$=>8000$

Hence, the value of $(-2)^3\times (-10)^3$ is $8000.$