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s344n2d4d5 [400]

2 years ago

13

Which of the following numbers is prime? 133 143 153 163

1 answer:

Elina [12.6K]2 years ago

4 0

133 is dividable by 7 to get 19
143 is dividable by 11 to get 13
153 is dividable by 3 to get 51
so the only number left is 163

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Determine the value of the variable in the product of powers.

aleksandrvk [35]

Answer:

<u><em>1. x = - 3</em></u>

<u><em>2. y = -9</em></u>

<u><em>3. n = 0</em></u>

<u><em></em></u>

Explanation:

The expressions are garbled. The correct expressions to determine the product of powers are:

1. What is the value of x in the product of powers $5^5\cdot 5^x=5^2$ ?

x =

2. What is the value of y in the product of $p^{-3}\cdot p^{-6}=p^y$ ?

y =

3. What is the value of n in th product of $9^2\cdot 9^{-7}\cdot 9^n=9^{-5}$ ?

n =

<h2>Solutions</h2>

<u />

<u>1. What is the value of x in the product of powers </u> $5^5\cdot 5^x=5^2$ <u> ?</u>

Apply the rule of the <em>product of powers with the same base</em> to the left side of the equality.

The product of two powers with the same base is the base raised to the sum of the exponent:

$5^5\cdot5^x=5^{(5+x)}$

Now the power on the left side has the same base as the power on the right side, so the exponents are the same:

5 + x = 2

x = 2 - 5

x = - 3

<u />

<u>2. What is the value of y in the product of </u> $p^{-3}\cdot p^{-6}=p^y$ <u> ?</u>

Again, the product of the two powers on the left side is equal to the common base raised to the sum of the exponents:

On the left side, you get:

$p^{-3}\cdot p^{-6}=p^{(-3-6)}=p^{-9}$

Then,

$p^{-9}=p^y\\\\-9=y\\\\y=-9$

3. What is the value of n in th product of $9^2\cdot 9^{-7}\cdot 9^n=9^{-5}$ ?

Same rule:

Left side:

$9^2\cdot 9^{-7}\cdot 9^n=9^{(2-7+n)}=9^{(-5+n)}$

Left side equal to right side:

$9^{(-5+n)}=9^{-5}\\\\-5+n=-5\\\\n=-5+5\\\\n=0$

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