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sukhopar [10]
3 years ago
11

Simplify this expression.

" title="\frac{4^{9} }{4^{3} }" alt="\frac{4^{9} }{4^{3} }" align="absmiddle" class="latex-formula">
Mathematics
2 answers:
Step2247 [10]3 years ago
6 0

Answer:

4⁹ / 4³ = 4⁶ = 4096

Step-by-step explanation:

You can solve this by realising that exponents (the 9 and the 3 in this case), simply tell you how many times to multiply the numbers together.

What you're see there then can also be expressed as:

\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4}{4 \times 4 \times 4}

Because the numerator and denominator are all multiples of the same number repeatedly, you can simply eliminate the bottom three fours from the top and bottom, giving you:

\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times (4 \times 4 \times 4)}{(4 \times 4 \times 4)}\\\\= 4 \times 4 \times 4 \times 4 \times 4 \times 4

4 \times 4 \times 4 \times 4 \times 4 \times 4

A simpler way to look at it is to understand that when the same number is being raised to different bases, and then multiplied or divided, you can simply add or subtract the exponents.  For example, speaking very generically:

x^a \times x^b = x^{a + b}

and

x^a \div x^b = x^{a - b}

In this case then, we can simply say:

\frac{4^9}{4^3} = 4^{9 - 3} = 4^6

So when simplified, the expression is equal to 4⁶, or 4096.

gogolik [260]3 years ago
3 0

9x9x9x9divide by 4x4x4

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7 0
3 years ago
In △PKQ, PK = KQ = 12, m∠P = 35º. Find PQ.
Neporo4naja [7]

The length of PQ is 19.66 units

Step-by-step explanation:

The given is:

1. PK = KQ = 12

2. m∠P = 35º

We need to find the length pf PQ

∵ PK = KQ

∴ m∠P = m∠Q

∵ m∠P = 35°

∴ m∠Q = 35°

The sum of measures of the angles of a triangle is 180°

∴ m∠P + m∠Q + m∠K = 180°

∴ 35 + 35 + m∠K = 180

∴ 70 + m∠K = 180

- Subtract 70 from both sides

∴ m∠K = 110°

Let us use cosine rule to find the length of PQ

∵ PQ = \sqrt{(KP)^{2}+(KQ)^{2}-2(KP)(KQ)cos(K)}

∵ PK = 12 , KQ = 12 , m∠K = 110°

- Substitute these values in the rule

∴ PQ = \sqrt{(12)^{2}+(12)^{2}-2(12)(12)cos(110)}

∴ PQ = 19.66

The length of PQ is 19.66 units

Learn more:

You can learn more about triangle in brainly.com/question/12985572

#LearnwithBrainly

4 0
3 years ago
Solve for y. ln(y-1)-ln2=x+ln x
alexandr402 [8]
ln(y - 1) - ln(2) = x + ln(x)
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2(\frac{1}{2}y - \frac{1}{2}) = 2xe^{x}
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3 0
3 years ago
22 students is__% of 55<br> Pls show me in steps
kramer

Answer:

40%

Step-by-step explanation:

divide the students by the total

22/55 = P

P = 0.4 = 40%

8 0
3 years ago
22. What is the measure of this line?
STALIN [3.7K]
Answer

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Step by step explanation
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