So here are a few rules with exponents that you should know:
- Multiplying exponents of the same base:

- Dividing exponents of the same base:

- Powering a power to a power:

- Converting a negative exponent to a positive one:

<h2>1.</h2>
Firstly, solve the outside exponent:

Next, convert the negative exponents into positive ones:

<u>Your final answer is
</u>
<h2>2.</h2>
For this, just divide:

<u>Your final answer is
</u>
<h2>3.</h2>
For this, convert all negative exponents into positive ones:

<u>Your final answer is
</u>
Given:
A circle with diameter 9 cm.
To find:
The area of the circle.
Solution:
The area of a circle is:
...(i)
Where r is the radius.
We know that, the diameter of a circle is twice than its radius.
The diameter of the given circle is 9 cm.


Substituting
in (i), we get




Therefore, the area of the given circle is 63.6.
Answer:
Step-by-step explanation:
Surface area = lateral area + 2(area of base)
Lateral area = perimeter of base * height.
Because it is a isosceles right triangle, both sides are equal.
= 72
2
= 72. Divide both sides by 2
= 36. Square both sides.
x = 6.
So the perimeter of the base = 6 + 6 +
= 20.485281374239
Lateral area = 20.485281374239 * 7 = 143.397 
Area of base is (1/2)base * height.
(1/2)(6)(6) = 18
Using the surface area formula
surface area = 143.397 + 2(18) = 179.4 
The equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x
<h3>How to evaluate the expression?</h3>
The expression is given as:
(8x)^-2/3 * (27x)^-1/3
Evaluate the exponent 8^-2/3
(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * (27x)^-1/3
Evaluate the exponent (27x)^-1/3
(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * 1/3(x)^-1/3
Multiply 1/4 and 1/3
(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^-2/3 * (x)^-1/3
Evaluate the exponent
(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-2/3 -1/3)
This gives
(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-1)
So, we have
(8x)^-2/3 * (27x)^-1/3 = 1/12x
Hence, the equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x
Read more about equivalent expression at
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Answer:
50% of 3000
Step-by-step explanation:
49% is very close to 50% (half). 3,025 pounds is very close to 3,000 pounds.
Half of 3,000 pounds is 1,500 pounds.