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Anna35 [415]
3 years ago
5

1.Simplify 5 to the 5th over 5 to the 8th.

Mathematics
2 answers:
disa [49]3 years ago
7 0

Answer:

it is (A) 1 over 5 to the 3rd power

Step-by-step explanation:

timurjin [86]3 years ago
3 0
Q1. The answer is <span>1 over 5 to the 3rd power.

</span>5 to the 5th is 5⁵
5 to the 8th is 5⁸
5 to the 5th over 5 to the 8th is \frac{ 5^{5} }{ 5^{8} }
To simplify, we will use two rules: 
\frac{ x^{a}}{ x^{b} } = x^{a-b} \\ x^{-a} = \frac{1}{ x^{a}}
Therefore:
\frac{ 5^{5} }{ 5^{8} } = 5^{5-8} =5^{-3}= \frac{1}{5^{3}}
\frac{1}{5^{3}} is the same as 1 over 5 to the 3rd power.


Q2. The answer is <span>(53)−4.

The exponents are multiplied when are expressed in the form:
</span>(x^{a}) ^{b}= x^{a*b}
So, (5^{3} )^{-4}=5^{3*(-4)}=5^{-12}

Other choices are incorrect:
<span>one third to the 4th times one third to the 7th is </span>( \frac{1}{3} )^{4} *( \frac{1}{3} )^{7}=( \frac{1}{3} )^{4+7}
3 to the 7th over 3 to the 15th is \frac{ 3^{7} }{3^{15}} =3^{7-15}
<span>45 ⋅ 42 is </span>4^{5}* 4^{2} =  4^{5+2}
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