Respuesta :
Answer:
[tex]8^{18}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]8^{15}[/tex] ÷ [tex]8^{-3}[/tex]
= [tex]8^{(15-(-3))}[/tex]
= [tex]8^{(15+3)}[/tex]
= [tex]8^{18}[/tex]
The simplified form is 8^18
What are Exponents?
The exponent of a number shows how many times the number is multiplied by itself. For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general, xn means that x is multiplied by itself for n times.
Properties of Exponents
The properties of exponents or laws of exponents are used to solve problems involving exponents. These properties are also considered as major exponents rules to be followed while solving exponents. The properties of exponents are mentioned below.
- Law of Product: am × an = am+n
- Law of Quotient: am/an = am-n
- Law of Zero Exponent: a0 = 1
- Law of Negative Exponent: a-m = 1/am
- Law of Power of a Power: (am)n = amn
- Law of Power of a Product: (ab)m = ambm
- Law of Power of a Quotient: (a/b)m = am/bm
Given:
8^15÷8^−3
Using
a^m / a^n = a^( m-n)
So,
8^15÷8^−3
=8^(15-(−3))
=8^(15 +3)
=8^18
Learn more about exponents and power here:
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