Question

Which number is the same as ?

A. -2

B. 1/8

C. 2

D. 32

E. 512

Answer 1

D. 32

Explanation:

Write the expression in exponential form with the base of 2

`2^(-2) x (2^(3) 4^(-2) )`

Calculate the quotient

`2^(-2) x 2^(7)`

2 ^ 5 = 32

Alternative form

32

Answer 2

Explanation:

`a^(-m)=(1)/(a^(m))\\\\(1)/(a^(-m))=a^(m)\\\\\\a^(m)*a^(n)=a^(m+n)\\\\(a^(m))/(a^(n))=a^(m-n)`

`(a^(m))^(n) = a^(m*n)`

In exponent multiplication, if two numbers have same base, just add the exponents

In exponent division, if two numbers have same base, just subtract the exponents

Prime factorize 4 = 2*2 = 2²

4⁻¹ *(2³÷ 4⁻² )= (2²)⁻¹ * ( 2³÷ (2²)⁻²

= (2⁻²)* (2³ ÷2⁻⁴)

`= 2^(-2) * (2^(3-[-4]))\\\\= 2^(-2) * (2^(3+4))\\\\= 2^(-2) * 2^(7)\\\\= 2^(-2+7)\\\\= 2^(5)\\\\= 2 * 2 * 2 * 2 * 2\\\\= 32`