Question

Which number is the same as ? A. -2 B. 1/8 C. 2 D. 32 E. 512

Answer 1

Answer:

Step-by-step explanation:

$a^{-m}=\frac{1}{a^{m}}\\\\\frac{1}{a^{-m}}=a^{m}\\\\\\a^{m}*a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}$

$(a^{m})^{n} = a^{m*n}$

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)

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

Answer 2

Answer:

D. 32

Step-by-step 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