Question

Simplify43 * 24 * 23182 * 20

Answer 1

`2^7`

Explanation:

Multiplication of factors with same base and different exponents:

Keep the base, add the exponents.

`x^a\ast x^b=x^(a+b)^{}`

Division of factors with same base and different exponents:

Keep the base, subtract the exponents.

`(x^a)/(x^b)=x^(a-b)`

Power of power:

Keep the base, multiply the exponents:

`(x^a)^b=x^(a\ast b)`

In this question:

`(4^3\ast2^4\ast2^3)/(8^2\ast2^0)=((2^2)^3\ast2^4\ast2^3)/((2^3)^2)=(2^6\ast2^4\ast2^3)/(2^6)=2^4^{}\ast2^3=2^(4+3)=2^7`