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2 years ago

Simplify 7^6 ⋅ 7^5. 49^11 49^35 7^11 7^35

Mathematics

2 answers:

Anna11 [10]2 years ago

5 0

<h3>Answer: 7^11</h3>

Explanation:

The rule is

a^b*a^c = a^(b+c)

Note how each base is the same (both 'a' each time). The rule wouldnt work if the bases were different.

So,

a^b*a^c = a^(b+c)

7^6 * 7^5 = 7^(6+5)

7^6 * 7^5 = 7^11

In short, you just add the exponents.

Keep in mind that the base stays at 7 the whole time. It might be tempting to do 7*7 = 49, but that would be incorrect.

Tatiana [17]2 years ago

3 0

Answer:

=8.310133e+125

Step-by-step explanation:

Given that:

= 7^6 ⋅ 7^5. 49^11 49^35 7^11 7^35

By making all bases same (equal to 7)

= 7^6 ⋅ 7^5. 7^2*11. 7^2*35. 7^11 7^35

=7^6 ⋅ 7^5. 7^22. 7^70. 7^11 7^35

As bases are same so powers will be added

=7^6+5+22+ 70+11+35

=7^149

=8.310133e+125

i hope it will help you!

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Can someone please write this as a single logarithm and show work please and thank you

Mazyrski [523]

Answer:

$log_b(w^3y^4)$

Step-by-step explanation:

To write the expression as a single logarithm, or condense it, use the properties of logarithms.

1) The power property of logarithms states that $log_ax^r = rlog_ax$ . In other words, the exponent within a logarithm can be brought out in front so it's multiplied by the logarithm. This means that the number in front of the logarithm can also be brought inside the logarithm as an exponent.

So, in this case, we can move the 3 and the 4 inside the logarithms as exponents. Apply this property as seen below:

$3log_bw+4log_by\\=log_bw^3+log_by^4$

2) The product property of logarithms states that $log_axy = log_ax+log_ay$ . In other words, the logarithm of a product is equal to the sum of the logarithms of its factors. So, in this case, write the expression as a single logarithm by taking the log (keep the same base) of the product of $w^3$ and $y^4$ . Apply the property as seen below and find the final answer.

$log_bw^3+log_by^4\\=log_b(w^3y^4)$

So, the answer is $log_b(w^3y^4)$ .

4 0

2 years ago

Find the cosine of both angle A and angle B.

Svetach [21]

We know that

cos A=adjacent side angle A/hypotenuse
adjacent side angle A=24 units
hypotenuse=26 units

cos A=24/26-----> 12/13

cos B=adjacent side angle B/hypotenuse
adjacent side angle B=10 units
hypotenuse=26 units

cos B=10/26------> 5/13

the answers are
cos A=12/13
cos B=5/13

cot A=adjacent side angle A/opposite side angle A
adjacent side angle A=24 units
opposite side angle A=10 units
cot A=24/10------> cot A=12/5

cot B=adjacent side angle B/opposite side angle B
adjacent side angle B=10 units
opposite side angle B=24 units
cot B=10/24------> cot B=5/12

8 0

2 years ago

Read 2 more answers

Help!

AnnyKZ [126]

Answer:

2 stars and 3 points

Step-by-step explanation:

8+2=10

10+4=14

14+6=20

the value increases by 2 each time.