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1 month ago

Which expression is equivalent to 15a^8b^4/5a^4b

Mathematics

2 answers:

AnnZ [12.3K]1 month ago

4 0

Response: The provided expression $\frac{15a^8b^4}{5a^4b}$ has been simplified to $3a^4b^3$

Detailed explanation:

Given: expression $\frac{15a^8b^4}{5a^4b}$

Our task is to simplify the given expression $\frac{15a^8b^4}{5a^4b}$

Let’s examine the given expression $\frac{15a^8b^4}{5a^4b}$

We divide the numbers $\frac{15}{5}=3$

$=\frac{3a^8b^4}{a^4b}$

Using the exponent rule, $\frac{x^a}{x^b}\:=\:x^{a-b}$

We get,

$\frac{a^8}{a^4}=a^{8-4}=a^4$

$=\frac{3a^4b^4}{b}$

Cancel the common factor b,

Thus, we have

$=3a^4b^3$

Therefore, the simplified version of the given expression $\frac{15a^8b^4}{5a^4b}$ is $3a^4b^3$

lawyer [12.5K]1 month ago

4 0

Response:

$\frac{15a^8b^4}{5a^4b}=3a^{4}b^{3}$

Detailed explanation:

Provided: Expression $\frac{15a^8b^4}{5a^4b}$

Objective: What is the simplified version of the expression?

Resolution:

Step 1 - Express the equation

$\frac{15a^8b^4}{5a^4b}$

Step 2 - Divide the numerator and denominator by 5

$=\frac{3a^8b^4}{a^4b}$

Step 3 - Implement the exponent rule, meaning $\frac{x^a}{x^b}\:=\:x^{a-b}$

$=3a^{8-4}b^{4-1}}$

$=3a^{4}b^{3}$

Consequently, the simplified form of the provided expression is

$\frac{15a^8b^4}{5a^4b}=3a^{4}b^{3}$

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lawyer [12517]

Answer:

A) The total duration needed to paint the room is 50 minutes.

B) To paint 64% of the room takes 32 minutes.

Step-by-step explanation:

Given as:

After 18 minutes, 64% of the room still requires painting.

Therefore, within 18 minutes, (100% - 64% = 36%) of the room has been painted

Let T minutes be the total time required to paint the entire room.

Now, according to the question

A ) Using the unitary method

∵ In total, 36% of the room is covered in 18 minutes

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Thus, T = 50 min

Therefore, the duration needed to paint the entire room = T = 50 minutes

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B) Again

Time taken to paint 64% of the room = x minutes

∵ 36% of the room has been painted in a total of 18 minutes

Thus, 1% of the entire room gets painted in $\dfrac{18}{36}$ minutes

Consequently, painting 64% of the room will take $\dfrac{18}{36}$ × 64 minutes

i.e x = $\dfrac{18\times 64}{36}$

Thus, x = 32 min

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Leona [12618]

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