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2 years ago

Index notation simplify 4^9 x 4^3

Mathematics

1 answer:

LenKa [72]2 years ago

7 0

Answer:

$4^{12}$

Step-by-step explanation:

Using the rule of exponents

$a^{m}$ × $a^{n}$ = $a^{(m+n)}$ , then

$4^{9}$ × $4^{3}$ = $4^{(9+3)}$ = $4^{12}$

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The volume of this prism

Licemer1 [7]

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3 years ago

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John has 12 pounds of dog food and is going to separate it into 3/4 pound portions. How many portions of dog food will he have?

NNADVOKAT [17]

16 portions

explanation:

12 / 3/4

= 12 * 4/3

= 4*4 = 16

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2 years ago

Please solve this, will rate 5 stars and mark as STAR!

Nina [5.8K]

Answer:

$\boxed{5 \cdot \sqrt{2} \cdot \sqrt[6]{5} }$

Step-by-step explanation:

$\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }$

$\sqrt{\sqrt[3]{10} } \implies (10^\frac{1}{3} )^\frac{1}{2} =10^\frac{1}{6} =\sqrt[6]{10}$

$\therefore \sqrt{\sqrt[3]{10} }=\sqrt[6]{10}$

$\text{Solving }\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }$

$250=2 \cdot 5^3$

$\sqrt[3]{250}=\sqrt[3]{2\cdot 5^3}=5 \sqrt[3]{2}$

Once

$\sqrt[6]{2} \cdot \sqrt[6]{5} = \sqrt[6]{10}$

We have

$5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5}$

We can proceed considering the common base of exponentials

$\sqrt[3]{2} \cdot \sqrt[6]{2} = 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} }=\sqrt{2}$

Therefore,

$5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5} = 5 \cdot \sqrt{2} \cdot \sqrt[6]{5}$

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3 years ago

In triangle QRS, QR = 8 and RS = 5. Which expresses all possible length of side QS?

VLD [36.1K]

Obviously it's answer D) Why?

a) any side of a triangle is SMALLER than the SUM of the 2 others

b) any side of a triangle is GREATER than the DIFFERENCE of the 2 others

Hence D) 8-5 < QS < 8+5==>3 < QS < 13

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3 years ago

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In the rectangle

LekaFEV [45]

In order to form triangle PQT and quadrilateral TQRS, point T must lie on line PS which is 16 cm. long.

If the ratio of PT to TS is 5:3 and the total length of PS is 16, then PT must be 10 and TS must be 6 (10 + 6 =16) and 10:6 is the same ratio as 5:3. Another way to think about it is 5/3 = 10/6.

Now you have all the lengths that you need to find the areas of the quadrilateral and the triangle.

Make sure you draw a diagram of it!!

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2 years ago

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