Question

Simplify and express in the exponential form by using laws of exponent:-​

Answer 1

Answer:

$\dfrac{ -1}{12500}$

Step-by-step explanation:

$\bigg[ \bigg( \dfrac{4}{ - 5} \bigg) ^{3} \div \bigg( \dfrac{ - 4}{5} \bigg)^{6} \bigg] \times \bigg( \dfrac{ - 4}{5} \bigg) ^{2}$

$= \displaystyle{ \bigg[ \bigg( \dfrac{4}{ - 5} \bigg) ^{3} \times \bigg( \frac{ - 5}{4} \bigg)^{6} \bigg ] \times \bigg( \dfrac{ - 4}{5} \bigg) ^{2}}$

$= \bigg[ \dfrac{ {4}^{3} }{ { - 5}^{3} } \times \dfrac{ { - 5}^{6} }{ {4}^{6}} \bigg] \times \bigg( \dfrac{ - 4}{5} \bigg) ^{2}$

$= \dfrac{ {(4)}^{3 - 6} }{ { (- 5)}^{6 - 3} } \times \bigg( \dfrac{ - 4}{5} \bigg) ^{2}$

$= \dfrac{ {4}^{ - 3} }{ { - 5}^{3} } \times \bigg( \dfrac{ - 4}{5} \bigg) ^{2}$

$= \dfrac{ {4}^{ - 3 + 2} }{ { - 5}^{3 + 2} }$

$= \dfrac{ {4}^{ - 1} }{ { - 5}^{5} }$

$= \dfrac{1}{4 \times { - 5}^{5} }$

$= \dfrac{1}{4 \times - 5 \times - 5 \times - 5 \times - 5 \times - 5}$

$= \dfrac{ -1}{12500}$

LAWS OF EXPONENT :

1. aᵐ × aⁿ = aᵐ ⁺ ⁿ
2. aᵐ ÷ aⁿ = aᵐ ⁻ ⁿ
3. a⁻ᵐ = 1/aᵐ
4. a⁻¹ = 1/a
5. (ab)ᵐ = aᵐ × bᵐ
6. (a/b)ᵐ = aᵐ / bᵐ
7. a⁰ = 1