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sergeinik [125]
3 years ago
13

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

Mathematics
2 answers:
MissTica3 years ago
8 0

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

GaryK [48]3 years ago
5 0

Answer:

D. 32

Step-by-step explanation:

Write the <u>expression</u> in exponential form with the <u>base</u> of 2

2^{-2} x (2^{3} 4^{-2} )

Calculate the <u>quotient</u>

2^{-2} x 2^{7}

2 ^ 5 = 32

<u>Alternative</u> form

32

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