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Sagot :
Given:
[tex]\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3[/tex]
To find:
The value of given expression by using the Laws of Exponents.
Solution:
We have,
[tex]\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3[/tex]
Using the Laws of Exponents, we get
[tex]=\left(-\dfrac{2}{3}\right)^{1+3}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]=\left(\dfrac{-2}{3}\right)^{4}[/tex]
[tex]=\dfrac{(-2)^4}{(3)^4}[/tex] [tex][\because \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}][/tex]
[tex]=\dfrac{(-2)\times (-2)\times (-2)\times (-2)}{(3)\times (3)\times (3)\times (3)}[/tex]
[tex]=\dfrac{16}{81}[/tex]
Therefore, the value of given expression is [tex]\dfrac{16}{81}[/tex].
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