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2 years ago

Please help with these two math problems 1. 7^x ÷ 7^y = 2. z^10x^y ÷ z^5 =

Mathematics

1 answer:

IceJOKER [234]2 years ago

8 0

Answer:

1. 7^(x-y)

2. z^5x^y

Step-by-step explanation:

The applicable rule of exponents is ...

(a^b)/(a^c) = a^(b-c)

$\dfrac{7^x}{7^y}=\boxed{7^{x-y}}$

$\dfrac{z^{10}x^y}{z^5}=x^yz^{10-5}=\boxed{z^5x^y}$

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Which pair shows equivalent expressions?

Dmitry_Shevchenko [17]

Which pair shows equivalent expressions?

A.2(2/5x + 2)=2 2/5x + 1

B.2(2/5x + 2)=4/5x + 4

C.2(2/5x + 4)=4/5x + 2

D.2(2/5x + 4)=2 2/5x + 8

Solution:

$2(\frac{2}{5}x + 2)$

Let us distribute 2 inside the parenthesis.

That is, we use distributive property:

a(b+c)=ab+ac

$2(\frac{2}{5}x + 2) =\frac{2*2}{5}x+2*2$

So, $2(\frac{2}{5}x + 2) =\frac{4}{5}x+4$

Answer:Option (b)

$2(\frac{2}{5}x+4)$

Applying distributive property, a(b+c)=ab+ac

$2(\frac{2}{5}x+4) =2*\frac{2}{5} x+2*4$

$2(\frac{2}{5}x+4) =\frac{2*2}{5} x+2*4$

$2(\frac{2}{5}x+4) =\frac{4}{5} x+8$

So, Option (B) is correct.

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2 years ago

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