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3 years ago

Simplify (5^3)^6 leaving your answer in index form

Mathematics

2 answers:

Verizon [17]3 years ago

5 0

$( {5}^{3} ) ^{6} = {5}^{3 \times 6} = {5}^{18}$

Temka [501]3 years ago

5 0

Answer:

5^18.

Step-by-step explanation:

By the law of indices:

(a^b)^c = a^(bc)

So (5^3)^6

= 5^(3*6)

= 5^18.

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Read 2 more answers

Ocean sunfish are well known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elap

Maksim231197 [3]

Answer:

Every day, the mass of the sunfish is multiplied by a factor of [ln(1.34)/6].

Step-by-step explanation:

You have the following function:

$M(t)=(1.34)^{\frac{t}{6}+4}$

To know what is the factor that multiplies the mass of the sunfish each day, you derivative the function M(t):

$\frac{dM(t)}{dt}=(1.34)^{\frac{t}{6}+4}(\frac{1}{6})ln(1.34)\\\\\frac{dM(t)}{dt}=\frac{ln(1.34)}{6}[(1.43)^{\frac{t}{6}+4}]\\\\\frac{dM(t)}{dt}=\frac{ln(1.34)}{6}M(t)$ (1)

where you have used the following general derivative:

$g(t)=a^{f(t)}\\g'(t)=a^{f(t)}f'(t)ln(a)$

The derivative give you the increase in the mass per day (because t is days). By the expression (1) you can conclude that each day the mass increase a factor of [ln(1.34)/6].

Every day, the mass of the sunfish is multiplied by a factor of [ln(1.34)/6].

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3 years ago