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\(4^ $5$ )( $4$ ^ $2$ )^ $3$ \

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Multiply powers: integer bases

Full solution

Q. \(4^

5

)(

4

^

2

)^

3

\

Identify Base and Exponents: Identify the base and the exponents in $(4^5)(4^2)^3$ . The base is $4$ . The exponents are $5$ for $4^5$ and $2$ for $4^2$ , which is then raised to the power of $3$ .
Simplify Exponents: Simplify $(4^2)^3$ by multiplying the exponents. $4^2$ raised to the power of $3$ is $4^{(2*3)}$ .
Calculate Exponent: Calculate $4^{(2*3)}$ . $4^{(2*3)}$ equals $4^6$ .
Combine Bases: Combine $4^5$ and $4^6$ by adding the exponents, since the bases are the same. $4^5 \times 4^6$ equals $4^{5+6}$ .
Calculate Final Result: Calculate $4^{(5+6)}$ . $4^{(5+6)}$ equals $4^{11}$ .

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