Answer :
By using power of a power rule, the result of [tex](4^{3} )^{2}[/tex] × [tex](\frac{1}{4} )^{2}[/tex] is 256.
What are exponential formulas?
Exponents formulas refer to the formulas that help solve exponents. Exponent of a number is represented in the form: [tex]x^{n}[/tex], meaning x is multiplied by itself for n times. Here,
x is called the "base"
n is called the "exponent" or "power"
[tex]x^{n}[/tex] is read as "x to the power of n" (or) "x raised to n"
Power of a power rule : [tex](a^{m} )^{n}=a^{mn}[/tex]
Given exponential expression
[tex](4^{3} )^{2}[/tex] × [tex](\frac{1}{4} )^{2}[/tex]
[tex](4^{3} )^{2}[/tex] is in the form of power of a power rule [tex](a^{m} )^{n}=a^{mn}[/tex]
= [tex]4^{6}[/tex] × [tex]\frac{1}{4^{2} }[/tex]
= [tex]4^{4}[/tex] × [tex]4^{2}[/tex] × [tex]\frac{1}{4^{2} }[/tex]
= [tex]4^{4}[/tex]
= 256
The result of [tex](4^{3} )^{2}[/tex] × [tex](\frac{1}{4} )^{2}[/tex] is 256.
Find out more information exponential formulas here
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