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MrRissso [65]
3 years ago
9

Evaluate (−23)×(−23)3 by using the Laws of Exponents

Mathematics
1 answer:
Nikolay [14]3 years ago
3 0

Given:

\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3

To find:

The value of given expression by using the Laws of Exponents.

Solution:

We have,

\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3

Using the Laws of Exponents, we get

=\left(-\dfrac{2}{3}\right)^{1+3}      [\because a^ma^n=a^{m+n}]

=\left(\dfrac{-2}{3}\right)^{4}

=\dfrac{(-2)^4}{(3)^4}      [\because \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}]

=\dfrac{(-2)\times (-2)\times (-2)\times (-2)}{(3)\times (3)\times (3)\times (3)}

=\dfrac{16}{81}

Therefore, the value of given expression is \dfrac{16}{81}.

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the home of bill burton is assessed at $91,000. the tax rate is 18.5 mills. what is the property tax on bills home?
IrinaVladis [17]

Answer:

  $1683.50

Step-by-step explanation:

You are expected to know that a "mill" is one thousandth of a dollar. In this context, it is the amount of tax on one dollar of assessed valuation. So, the tax amount is found by multiplying the valuation by 18.5/1000:

  tax = 0.0185 · $91,000 = $1683.50

6 0
3 years ago
Find the lateral area of the cone in terms of π.
Andreyy89

Answer:

15\pi\ cm^{2}

Step-by-step explanation:

we know that

The lateral area of the cone is equal to

LA=\pi rl

where

r is the radius of the base

l is the slant height

we have

r=3\ cm

Applying the Pythagoras Theorem find the slant height

l^{2}=3^{2} +4^{2}\\ \\l^{2}=25\\ \\l=5\ cm

substitute in the formula

LA=\pi (3)(5)=15\pi\ cm^{2}

8 0
3 years ago
Given cos x=0.4762,find the degree measure of x.round your answer to the nearest tenth
alex41 [277]

If you have a calculator, you can use the inverse cos " cos⁻¹ " key. Many upper level books write that as Arccos so as not to confuse you with a negative exponent. We do that because if you take the cosine of any angle, and then the inverse cosine of any angle, it leads you back to the original angle. Think of it as a big "UNDO" button.

To one decimal place, that result is 61.6 degrees.

5 0
3 years ago
Julie sent 200 emails last month. This month she sent 40% less. How many
NeX [460]

Answer:

She sent 120 emails this month.

Step-by-step explanation:

Multiply 200 by .60 (60 percent) and it will give you 120.

I used 60 instead of 40 because the problem said 40 percent less, NOT 40 percent of 200.

8 0
2 years ago
Every night Nathan has to read at least 25 minutes. Write an inequality that shows how long Nathan can read each night
DaniilM [7]

Answer:

25<=x

i need 20 characters to answer

3 0
3 years ago
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