Answer:
[tex]=\frac{64}{3v}[/tex]
Step-by-step explanation:
One is given the following equation:
[tex]\frac{(4v^-^3)^3}{3v^-^8}[/tex]
Simplify the numerator, remember to raise every number inside the parenthesis to the exponent outside of the parenthesis. Bear in mind, an exponent raised to another exponent is equal to the exponent times the exponent it is raised to. Then simplify by multiplying the number by itself the number of times that the exponent indicates.
[tex]\frac{(4v^-^3)^3}{3v^-^8}[/tex]
[tex]=\frac{4^3(v^-^3)^3}{3v^-^8}[/tex]
[tex]=\frac{4^3v^-^9}{3v^-^8}[/tex]
[tex]=\frac{64v^-^9}{3v^-^8}[/tex]
Bring the variable (v) in the denominator (value under the fraction bar) to the numerator (value ontop of the fraction bar) by multiplying its exponent by (-1). This can be done simply because all operations in this equation are multiplication or division, remember, an exponent is another form of multiplication.
[tex]=\frac{64v^-^9}{3v^-^8}[/tex]
[tex]=\frac{(64v^-^9)(v^(^-^1^)^(^-^8^))}{3}[/tex]
Simplify, remember, multiplying two numbers with the same base that have an exponent is the same as adding the two exponents,
[tex]=\frac{(64v^-^9)(v^(^-^1^)^(^-^8^))}{3}[/tex]
[tex]=\frac{(64v^-^9)(v^8)}{3}[/tex]
[tex]=\frac{64v^-^9^+^8)}{3}[/tex]
[tex]=\frac{64v^-^1}{3}[/tex]
Now bring the variable to the denominator so that there are no negative exponents. Use a similar technique that was used to bring variables with exponents to the numerator.
[tex]=\frac{64v^-^1}{3}[/tex]
[tex]=\frac{64}{3(v^(^-^1^)^(^-^1^))}[/tex]
[tex]=\frac{64}{3v^1}[/tex]
[tex]=\frac{64}{3v}[/tex]
