Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Answer 1

Answer:

(a)

$5^{-3}=\frac{1}{125}$

(b)

$-5^{-3}=-\frac{1}{125}$

(c)

$(-5^{-3})^{-1}=-125$

(d)

$(-5^{-3})^{0}=1$

Step-by-step explanation:

(a)

$5^{-3}$

we can use property of exponent

$a^{-n}=\frac{1}{a^n}$

we get

$5^{-3}=\frac{1}{5^3}$

$5^{-3}=\frac{1}{5\times 5\times 5}$

$5^{-3}=\frac{1}{125}$........Answer

(b)

$-5^{-3}$

we can use property of exponent

$a^{-n}=\frac{1}{a^n}$

we get

$-5^{-3}=-\frac{1}{5^3}$

$-5^{-3}=-\frac{1}{5\times 5\times 5}$

$-5^{-3}=-\frac{1}{125}$........Answer

(c)

$(-5^{-3})^{-1}$

we can use property of exponent

$(a^{n})^m=a^{m\times n}$

we get

$(-5^{-3})^{-1}=(-5)^{-3\times -1}$

$(-5^{-3})^{-1}=(-5)^3$

$(-5^{-3})^{-1}=(-5)\times (-5)\times (-5)$

$(-5^{-3})^{-1}=-125$........Answer

(d)

$(-5^{-3})^{0}$

we can use property of exponent

$(a^{n})^m=a^{m\times n}$

we get

$(-5^{-3})^{0}=(-5)^{-3\times 0}$

$(-5^{-3})^{-1}=(-5)^0$

we can use property

$a^0=1$

$(-5^{-3})^{0}=1$........Answer