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Mathematics

1 answer:

vladimir2022 [97]3 years ago

7 0

-9...................

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I have asked so many times and no one will answer. :(

andrew-mc [135]

Answer:

1) $\frac{1}{2^7}$ ; 2) $11^7$

Step-by-step explanation:

1) Using the Power of a Fraction Rule $(\frac{a}{b} )^x = (\frac{a^x}{b^x} )$ ,

$(\frac{1}{2} )^7 = (\frac{1^7}{2^7} )$ , which can just be simplified to $\frac{1}{2^7}$ .

2) Using the Negative Exponent Rule, $a^{-x} = \frac{1}{a^{x}}$ ,

$(\frac{1}{11} )^{-7} = \frac{1}{\frac{1}{11^7}}$ , which can be simplified to $11^7$ .

4 0

3 years ago

Log*subscript*(3x − 2) 4096 = 3<br><br> I got x= negative 6 is this correct??

Brut [27]

Remember

$log_a(b)=c$ translates to $a^c=b$
and
$log_a(b^c)=clog_a(b)$
so

4096=16^3
$log_{3x-2}(4096)=3$
$log_{3x-2}(16^3)=3$
$3log_{3x-2}(16)=3$
divide both sides by 3
$log_{3x-2}(16)=1$
translate
$(3x-2)^1=16$
3x-2=16
add 2 to both sides
3x=18
divide both sides by 3
x=6

8 0

4 years ago

12x+7<-11 or 5x-8>40

puteri [66]

Answer:

$\large\boxed{x9\dfrac{3}{5}\to x\in\left(-\infty,\ -1\dfrac{1}{2}\right)\ \cup\ \left(9\dfrac{3}{5},\ \infty\right)}$

Step-by-step explanation:

$12x+7$

$5x-8>40\qquad\text{add 8 to both sides}\\\\5x-8+8>40+8\\\\5x>48\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}>\dfrac{48}{5}\\\\x>\dfrac{48}{5}\\\\x>9\dfrac{3}{5}\\===========================$