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\(4^ $6$ )( $4$ ^{ $-8$ })\

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Multiply powers: integer bases

Full solution

Q. \(4^

6

)(

4

^{

-8

})\

Identify Base and Exponents: Identify the base and the exponents in the expression $(4^6)(4^{-8})$ . In the expression $4^6$ , $4$ is the base raised to the exponent $6$ . In the expression $4^{-8}$ , $4$ is the base raised to the exponent $-8$ .
Base: $4$
Exponents: $6$ , $-8$
Rewrite as Single Power: Rewrite $(4^6)(4^{-8})$ as a single power of $4$ . When we multiply powers with the same base, we add the exponents. $\newline$ $(4^6)(4^{-8}) = 4^{6 + (-8)} = 4^{-2}$
Simplify Expression: Simplify the expression $4^{-2}$ . A negative exponent means that the base is on the denominator and the exponent is positive. $\newline$ $4^{-2} = \frac{1}{4^2} = \frac{1}{16}$

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