Question

Apply the properties of integer exponents to identify all of the expressions equivalent to 1 32 . A.2−5 B. 1/2^5 C. 2^4/2^9 D.2^2 + 2^−7 E.2^5 × 2^−10

Answer 1

If you were looking for multiple answers, then I only found one. E.2⁵ * 2⁻¹⁰ is the only correct answer from my perspective. When you do the math, you get a long, huge decimal times 32, and you'd get 1/32. Hope this helps!

Answer 2

Answer:

The Properties of integer exponents to identify for all expressions A,B,C,E accept the condition. but the D is not accepting the condition.

Step-by-step explanation:

Property 1 :

If two terms are multiplied with the same base, the base has to be taken once and exponents have to be added.  

$x^{m} \cdot x^{n}=x^{m+n}$

Property 2 :

If two terms are in division with the same base, the base has to be taken once and exponents have to be subtracted.

$x^{m} \div x^{n}=x^{m-n}$

Property 3 :

If there is an exponent for an exponential term, two exponents can either be multiplied or interchanged.

$\left(x^{m}\right)^{n}=x^{m n} \\or\\ \left(x^{m}\right)^{n}=\left(x^{n}\right)^{m}$

Property 4 :

If there is a common exponent for the product of two or more terms, the exponent can be distributed to each term.  

$\left(xy^{m})=x^{m}.y^{m}$

Property 5 :

If there is a common exponent for two terms in division, the exponent can be distributed to each term.  $(\frac{x}{y})^{m}}=\frac{x^{m}}{y^{m}}$

Property 6 :

If a term is moved from numerator to denominator or denominator to numerator, the sign of the exponent has to be changed.

$x^{-m} =\frac{1}{x^m}$

Property 7 :

For any base, if the exponent is zero, its value is 1.

$x^{0}=1$

Property 8 :

For any base base, if there is no exponent, the exponent is assumed to be 1.

$x=x^{1}$

A.

$2^{-5}=\\ Apply\ the\ property\ 6\\ x^{-m}=\frac{1}{x^{m}}\\Now,\\2^{-5}=\frac{1}{2^{5}}\\\\=\frac{1}{32}$

B.$\frac{1}{ 2^{5}}\\Now,=\frac{1}{2^{5}}\\\\=\frac{1}{32}$

C.$\frac{2^{4}}{2^{9}}\\ Applying \ property\ 2\\\\x^{m} \div x^{n}=x^{m-n} \\2^{4} \div 2^{9}=2^{4-9}\\=2^{-5}\\Applying\ property\ 6 \\\frac{1}{2^{5}} \\=\frac{1}{32}$

D it is not satisfying the properties of exponents

E.$2^5 * 2^-{10}\\=2^{5+-10}\\=2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}$