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<h2>
Answer:</h2>
<h2>
Step-by-step explanation:</h2>
a. 2x^-3 • 4x^2
To solve this using only positive exponents, follow these steps:
i. Rewrite the expression in a clearer form
2x⁻³ . 4x²
ii. The position of the term with negative exponent is changed from denominator to numerator or numerator to denominator depending on its initial position. If it is at the numerator, it is moved to the denominator. If otherwise it is at the denominator, it is moved to the numerator. When this is done, the negative exponent is changed to positive.
In our case, the first term has a negative exponent and it is at the numerator. We therefore move it to the denominator and change the negative exponent to positive as follows;
iii. We then solve the result as follows;
=
Therefore, 2x⁻³ . 4x² =
b. 2x^4 • 4x^-3
i. Rewrite as follows;
2x⁴ . 4x⁻³
ii. The second term has a negative exponent, therefore swap its position and change the negative exponent to a positive one.
iii. Now solve by cancelling out common terms in the numerator and denominator. So we have;
Therefore, 2x⁴ . 4x⁻³ =
c. 2x^3y^-3 • 2x
i. Rewrite as follows;
2x³y⁻³ . 2x
ii. Change position of terms with negative exponents;
iii. Now solve;
Therefore, 2x³y⁻³ . 2x =
The properties that were used
to derive the properties of logarithms are the properties of exponent because
logarithms are exponents. The properties of exponents are: product of powers,
power to a power, quotient of powers, power f a product and power of a
quotient.
As an example, the log
property log(a^k) = k log (a) can be derived from the exponential property
(b^a)^k = b^(ak).
Likewise,
log (ab) = log (a) + log (b) comes from c^(a+b) = c^a*c^b
Proof:
Let x = c^a and y=c^b
Then,
log (x) = a and log (y) =
b (base c)
<span>log (xy) = log (c^a * c^b) =
log (c^(a+b)) = a+b = log(x) + log (y)</span>
The number of remaining problems is:
30-20 = 10 problems.
The amount of time remaining is:
40-25 = 15minutes
For the first 20 problems the time per problem is:
t1 = 25/20 = 5/4 minutes
For the remaining problems the time per problem is:
t2 = 15/10 = 3/2 minutes
Answer:
you will be able to spend about 3/2 minutes on each remaining problem
Answer:
Step-by-step explanation: