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4 years ago

Simplify ( 8∙4∙2 8∙7 )^2 × ( 8 0 7−3 )^3 × 7 −9 .

1 answer:

4 0

$\bf ~\hspace{7em}\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
~\hspace{4.5em}
a^n\implies \cfrac{1}{a^{-n}}
~\hspace{4.5em}
\cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\left( \cfrac{8\cdot 4\cdot 2}{8\cdot 7} \right)^2\times \left( \cfrac{8^0}{7^{-3}} \right)^3\times 7^{-9}\implies \left( \cfrac{8\cdot 8}{8\cdot 7} \right)^2\times \left( \cfrac{1\cdot 7^3}{1} \right)^3\times \cfrac{1}{7^9}$

$\bf \left( \cfrac{8}{8}\cdot \cfrac{8}{7} \right)^2\times (7^3)^3\times \cfrac{1}{7^9}\implies \left( \cfrac{8}{7} \right)^2\times 7^{3\cdot 3}\times \cfrac{1}{7^9}\implies \cfrac{8^2}{7^2}\times \cfrac{7^9}{7^9}
\\\\\\
\cfrac{8^2}{7^2}\implies \cfrac{64}{49}$

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Drag the tiles to the correct boxes to complete the pairs. Find the distance between each pair of points. 5 units 4 units 2 unit

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Answer:

a) Distance between points A (5, 4) and B( 5, -2) is 6 units

b) Distance between points E (-2, -1) and F( -2, -5) is 4 units

c) Distance between points C (-4, 1) and D( 1, 1) is 5 units

d) Distance between points G(3, -5) and H(6, -5) is 3 units

Step-by-step explanation:

We need to find the distance between each pair

a) A (5, 4) and B( 5, -2)

the distance formula is:

$d(A,B) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Putting values: x₁ = 5, x₂=5 and y₁= 4 and y₂= -2

$d(A,B) = \sqrt{(5-5)^2+(-2-4)^2}$

$d(A,B) = \sqrt{(0)^2+(-6)^2}$

$d(A,B) = \sqrt{36}$

$d(A,B) = 6$

Distance between points A (5, 4) and B( 5, -2) is 6 units

b) E (-2, -1) and F( -2, -5)

the distance formula is:

$d(E,F) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Putting values: x₁ = -2, x₂=-2 and y₁= -1 and y₂= -5

$d(E,F) = \sqrt{(-2-(-2))^2+(-5-(-1))^2}$

$d(E,F) = \sqrt{(0)^2+(-4)^2}$

$d(E,F) = \sqrt{16}$

$d(E,F) = 4$

Distance between points E (-2, -1) and F( -2, -5) is 4 units

c) C (-4, 1) and D( 1, 1)

the distance formula is:

$d(C,D) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Putting values: x₁ = -4, x₂=1 and y₁= 1 and y₂= 1

$d(C,D)= \sqrt{(1-(-4))^2+(1-(1))^2}$

$d(C,D) = \sqrt{(5)^2+(0)^2}$

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$d(C,D) = 5$

Distance between points C (-4, 1) and D( 1, 1) is 5 units

d) G(3, -5) and H(6, -5)

the distance formula is:

$d(G,H) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Putting values: x₁ = 3, x₂=6 and y₁= -5 and y₂= -5

$d(G,H)= \sqrt{(6-(3))^2+(-5-(-5))^2}$

$d(G,H) = \sqrt{(3)^2+(0)^2}$

$d(G,H) = \sqrt{9}$

$d(G,H) = 3$

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